References
-
T. Akahori, A new approach to the local embedding theorem of CR-structures for n
$\geq$ 4 (the local solvability for the operator$ \partial$ b in the abstract sense), Mem. Amer. Math. Soc. 67 (1987), no. 366, xvi+257 pp - G. Aladro, The comparability of the Kobayashi approach region and the admissible approach region, Illinois J. Math. 33 (1989), no. 1, 42-63
- E. Bedford and J. Dadok, Bounded domains with prescribed group of automorphisms, Comment. Math. Helv. 62 (1987), no. 4, 561-572 https://doi.org/10.1007/BF02564462
-
E. Bedford and S. Pinchuk, Domains in
$C^n+1$ with noncompact automorphism group, J. Geom. Anal. 1 (1991), no. 3, 165-191 https://doi.org/10.1007/BF02921302 -
E. Bedford and S. Pinchuk, Domains in
$C^2$ with noncompact automorphism groups, Indiana Univ. Math. J. 47 (1998), no. 1, 199-222 -
S. R. Bell, Biholomorphic mappings and the
$\partial$ -problem, Ann. of Math. (2) 114 (1981), no. 1, 103-113 https://doi.org/10.2307/1971379 - S. Bell and E. Ligocka, A simplification and extension of Fefferman's theorem on biholomorphic mappings, Invent. Math. 57 (1980), no. 3, 283-289 https://doi.org/10.1007/BF01418930
-
F. Berteloot, Characterization of models in
$C^2$ by their automorphism groups, Internat. J. Math. 5 (1994), no. 5, 619-634 https://doi.org/10.1142/S0129167X94000322 -
T. Bloom and I. Graham, A geometric characterization of points of type m on real submanifolds of
$C^n$ , J. Differential Geometry 12 (1977), no. 2, 171-182. https://doi.org/10.4310/jdg/1214433979 - H. Boas, E. Straube, and J. Yu, Boundary limits of the Bergman kernel and metric, Michigan Math. J. 42 (1995), no. 3, 449-461 https://doi.org/10.1307/mmj/1029005306
- A. Bogges, CR Manifolds and the Tangential Cauchy-Riemann Complex, Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1991
- D. Burns, S. Shnider, and R. O. Wells, Deformations of strictly pseudoconvex domains, Invent. Math. 46 (1978), no. 3, 237-253 https://doi.org/10.1007/BF01390277
- J. Byun, On the automorphism group of the Kohn-Nirenberg domain, J. Math. Anal. Appl. 266 (2002), no. 2, 342-356 https://doi.org/10.1006/jmaa.2001.7736
- J. Byun, On the boundary accumulation points for the holomorphic automorphism groups, Michigan Math. J. 51 (2003), no. 2, 379-386 https://doi.org/10.1307/mmj/1060013203
- J. Byun and H. Gaussier, On the compactness of the automorphism group of a domain, C. R. Math. Acad. Sci. Paris 341 (2005), no. 9, 545-548 https://doi.org/10.1016/j.crma.2005.09.018
- J. Byun, H. Gaussier, and K.-T. Kim, Weak-type normal families of holomorphic mappings in Banach spaces and characterization of the Hilbert ball by its automorphism group, J. Geom. Anal. 12 (2002), no. 4, 581-599 https://doi.org/10.1007/BF02930654
- D. Catlin, Estimates of invariant metrics on pseudoconvex domains of dimension two, Math. Z. 200 (1989), no. 3, 429-466 https://doi.org/10.1007/BF01215657
- S. S. Chern and J. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271 https://doi.org/10.1007/BF02392146
-
M. Christ, Regularity properties of the
$\partial$ b equation on weakly pseudoconvex CR manifolds of dimension 3, J. Amer. Math. Soc. 1 (1988), no. 3, 587-646 https://doi.org/10.2307/1990950 - J. P. D'Angelo, Several Complex Variables and the Geometry of Real Hypersurfaces, CRC Press, Boca Raton, FL, 1993
- J. P. D'Angelo, A gentle introduction to points of finite type on real hypersurfaces, Explorations in complex and Riemannian geometry, 19-36, Contemp. Math., 332, Amer. Math. Soc., Providence, RI, 2003 https://doi.org/10.1090/conm/332/05928
- J. P. D'Angelo and J. J. Kohn, Subelliptic estimates and finite type, Several complex variables (Berkeley, CA, 1995-1996), 199-232, Math. Sci. Res. Inst. Publ., 37, Cambridge Univ. Press, Cambridge, 1999
- K. Diederich and J. E. Fornaess, Pseudoconvex domains with real-analytic boundary, Ann. Math. (2) 107 (1978), no. 2, 371-384 https://doi.org/10.2307/1971120
- K. Diederich and S. Pinchuk, Reflection principle in higher dimensions, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Doc. Math. 1998, Extra Vol. II, 703-712
- P. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, 259. Springer-Verlag, New York, 1983
- V. Ejov and A. Isaev, On the dimension of the stability group for a Levi non-degenerate hypersurface, Illinois J. Math. 49 (2005), no. 4, 1155-1169
- V. Ezhov, Linearization of automorphisms of a real-analytic hypersurface, Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985), no. 4, 731-765
- C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65 https://doi.org/10.1007/BF01406845
- C. Fefferman and J. Kohn, Holder estimates on domains of complex dimension two and on three-dimensional CR manifolds, Adv. in Math. 69 (1988), no. 2, 223-303 https://doi.org/10.1016/0001-8708(88)90002-3
- S. Frankel, Complex geometry of convex domains that cover varieties, Acta Math. 163 (1989), no. 1-2, 109-149 https://doi.org/10.1007/BF02392734
- S. Fu, Asymptotic expansions of invariant metrics of strictly pseudoconvex domains, Canad. Math. Bull. 38 (1995), no. 2, 196-206 https://doi.org/10.4153/CMB-1995-028-9
- H. Gaussier and A. Sukhov, On the geometry of model almost complex manifolds with boundary, Math. Z. 254 (2006), no. 3, 567-589 https://doi.org/10.1007/s00209-006-0959-1
- H. Gaussier and A. Sukhov, Estimates of the Kobayashi-Royden metric in almost complex manifolds, Bull. Soc. Math. France 133 (2005), no. 2, 259-273 https://doi.org/10.24033/bsmf.2486
- I. Graham, Boundary behavior of the Caratheodory and Kobayashi metrics on strongly pseudoconvex domains in Cn with smooth boundary, Trans. Amer. Math. Soc. 207 (1975), 219-240 https://doi.org/10.2307/1997175
-
R. E. Greene and S. G. Krantz, Deformation of complex structures, estimates for the
$\partial$ equation, and stability of the Bergman kernel, Adv. in Math. 43 (1982), no. 1, 1-86 https://doi.org/10.1016/0001-8708(82)90028-7 - R. E. Greene and S. G. Krantz, Characterizations of certain weakly pseudoconvex domains with noncompact automorphism groups, Complex analysis (University Park, Pa., 1986), 121-157, Lecture Notes in Math., 1268, Springer, Berlin, 1987
- R. E. Greene and S. G. Krantz, Biholomorphic self-maps of domains, Complex analysis, II (College Park, Md., 1985-86), 136-207, Lecture Notes in Math., 1276, Springer, Berlin, 1987
- R. E. Greene and S. G. Krantz, The automorphism groups of strongly pseudoconvex domains, Math. Ann. 261 (1982), no. 4, 425-446 https://doi.org/10.1007/BF01457445
-
R. E. Greene and S. G. Krantz, Invariants of Bergman geometry and the automorphism groups of domains in
$C^n$ , Geometrical and algebraical aspects in several complex variables (Cetraro, 1989), 107-136, Sem. Conf., 8, EditEl, Rende, 1991 - R. E. Greene and S. G. Krantz, Geometric foundations for analysis on complex domains, Proc. of the 1994 Conference in Cetraro (D. Struppa, ed.), 1995
- M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307-347 https://doi.org/10.1007/BF01388806
- S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962
-
L. Hormander,
$L^2$ estimates and existence theorems for the$\partial$ operator, Acta Math. 113 (1965), 89-152 https://doi.org/10.1007/BF02391775 - L. K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, American Mathematical Society, Providence, 1963
- X. Huang, Schwarz reflection principle in complex spaces of dimension two, Comm. Partial Differential Equations 21 (1996), no. 11-12, 1781-1828 https://doi.org/10.1080/03605309608821246
- A. Huckleberry and E. Oeljeklaus, Classification Theorems for Almost Homogeneous Spaces, Institut Elie Cartan, 9. Universite de Nancy, Institut Elie Cartan, Nancy, 1984
- A Isaev and S. G. Krantz, Domains with non-compact automorphism group: a survey, Adv. Math. 146 (1999), no. 1, 1-38 https://doi.org/10.1006/aima.1998.1821
- A. V. Isaev and N. G. Kruzhilin, Effective actions of the unitary group on complex manifolds, Canad. J. Math. 54 (2002), no. 6, 1254-1279 https://doi.org/10.4153/CJM-2002-048-2
- K.-T. Kim, Domains in Cn with a piecewise Levi flat boundary which possess a noncompact automorphism group, Math. Ann. 292 (1992), no. 4, 575-586 https://doi.org/10.1007/BF01444637
- K.-T. Kim, On the automorphism groups of convex domains in Cn, Adv. Geom. 4 (2004), no. 1, 33-40 https://doi.org/10.1515/advg.2004.005
- K.-T. Kim, Asymptotic behavior of the curvature of the Bergman metric of the thin domains, Pacific J. Math. 155 (1992), no. 1, 99-110 https://doi.org/10.2140/pjm.1992.155.99
- K.-T. Kim and S.-Y. Kim, CR hypersurfaces with a weakly-contracting automorphism, J. Geom. Anal. (To appear)
- K.-T. Kim and S. G. Krantz, Complex scaling and domains with non-compact automorphism group, Illinois J. Math. 45 (2001), no. 4, 1273-1299
- K.-T. Kim and S. G. Krantz, Characterization of the Hilbert ball by its automorphism group, Trans. Amer. Math. Soc. 354 (2002), no. 7, 2797-2818 https://doi.org/10.1090/S0002-9947-02-02895-7
-
K.-T. Kim, S. G. Krantz, and A. Spiro, Analytic polyhedra in
$C^2$ with a non-compact automorphism group, J. Reine Angew. Math. 579 (2005), 1-12 - K.-T. Kim and S. Lee, Asymptotic behavior of the Bergman kernel and associated invariants in certain infinite type pseudoconvex domains, Forum Math. 14 (2002), no. 5, 775-795 https://doi.org/10.1515/form.2002.033
- K.-T. Kim and D. Ma, A note on: 'Characterization of the Hilbert ball by its automorphisms' J. Korean Math. Soc. 40 (2003), no. 3, 503-516 https://doi.org/10.4134/BKMS.2003.40.3.503
- K.-T. Kim and D. Ma, A note on: 'Characterization of the Hilbert ball by its automorphisms' MR1973915, J. Math. Anal. Appl. 309 (2005), no. 2, 761-763 https://doi.org/10.1016/j.jmaa.2004.09.024
-
K.-T. Kim and A. Pagano, Normal analytic polyhedra in
$C^2$ with a noncompact automorphism group, J. Geom. Anal. 11 (2001), no. 2, 283-293 https://doi.org/10.1007/BF02921967 - K.-T. Kim and G. Schmalz, Dynamics of local automorphisms of embedded CRmanifolds, Mat. Zametki 76 (2004), no. 3, 477-480 https://doi.org/10.4213/mzm575
- K.-T. Kim and G. Schmalz, Dynamics of local automorphisms of embedded CRmanifolds, Mtranslation in Math. Notes 76 (2004), no. 3-4, 443-446 https://doi.org/10.1023/B:MATN.0000043473.56503.f3
- K.-T. Kim and J. Yu, Boundary behavior of the Bergman curvature in strictly pseudoconvex polyhedral domains, Pacific J. Math. 176 (1996), no. 1, 141-163 https://doi.org/10.2140/pjm.1996.176.141
- P. Klembeck, Kahler metrics of negative curvature, the Bergmann metric near the boundary, and the Kobayashi metric on smooth bounded strictly pseudoconvex sets, Indiana Univ. Math. J. 27 (1978), no. 2, 275-282 https://doi.org/10.1512/iumj.1978.27.27020
- S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York, 1970
- S. Kobayashi, Transformation Groups in Differential Geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70, Springer-Verlag, New York-Heidelberg, 1972
-
J. J. Kohn, Boundary behavior of
$\delta$ on weakly pseudo-convex manifolds of dimension two, J. Differential Geometry 6 (1972), 523-542 https://doi.org/10.4310/jdg/1214430641 - J. J. Kohn and L. Nirenberg, A pseudo-convex domain not admitting a holomorphic support function, Math. Ann. 201 (1973), 265-268 https://doi.org/10.1007/BF01428194
- S. G. Krantz, Function Theory of Several Complex Variables, American Mathematical Society, Providence, RI, 2000
- S. G. Krantz, Calculation and estimation of the Poisson kernel, J. Math. Anal. Appl. 302 (2005), no. 1, 143-148 https://doi.org/10.1016/j.jmaa.2004.08.010
- S. G. Krantz, Partial Differential Equations and Complex Analysis, CRC Press, Boca Raton, FL, 1992
- N. Kruzhilin and A. V. Loboda, Linearization of local automorphisms of pseudoconvex surfaces, Dokl. Akad. Nauk SSSR 271 (1983), no. 2, 280-282
- M. Kuranishi, Strongly pseudoconvex CR structures over small balls. III. An embedding theorem, Ann. of Math. (2) 116 (1982), no. 2, 249-330 https://doi.org/10.2307/2007063
- M. Landucci, The automorphism group of domains with boundary points of infinite type, Illinois J. Math. 48 (2004), no. 3, 875-885
-
M. Landucci and G. Patrizio, Unbounded domains in
$C^2$ with non-compact automorphisms group, Results Math. 42 (2002), no. 3-4, 300-307 https://doi.org/10.1007/BF03322857 - K. H. Lee, Automorphism groups of almost complex manifolds, Ph. D. dissertation, Pohang University of Science and Technology (POSTECH), Pohang 790-784 Korea, (2005), 97 pages
- K. H. Lee, Almost complex manifolds and Cartan's uniqueness theorem, Trans. Amer. Math. Soc. 358 (2006), no. 5, 2057-2069 https://doi.org/10.1090/S0002-9947-05-03973-5
- K. H. Lee, Domains in almost complex manifolds with an automorphism orbit accumulating at a strongly pseudoconvex boundary point, Michigan Math. J. 54 (2006), no. 1, 179-205 https://doi.org/10.1307/mmj/1144437443
- K. H. Lee, Strongly pseudoconvex domains in almost complex manifolds, J. Reine Angew. Math. (To appear.)
-
S. Lee, Asymptotic behavior of the Kobayashi metric on certain infinite-type pseudoconvex domains in
$C^2$ , J. Math. Anal. Appl. 256 (2001), no. 1, 190-215 https://doi.org/10.1006/jmaa.2000.7307 - D. Ma, Sharp estimates of the Kobayashi metric near strongly pseudoconvex points, The Madison Symposium on Complex Analysis (Madison, WI, 1991), 329-338, Contemp. Math., 137, Amer. Math. Soc., Providence, RI, 1992
- X. Ma and G. Marinescu, Generalized Bergman kernels on symplectic manifolds, C. R. Math. Acad. Sci. Paris 339 (2004), no. 7, 493-498 https://doi.org/10.1016/j.crma.2004.07.016
- X. Ma and G. Marinescu, Holomorphic Morse Inequalities and Bergman Kernels, Progress in Mathematics, 254. Birkhauser Verlag, Basel, 2007
-
J. McNeal, Boundary behavior of the Bergman kernel function in
$C^2$ , Duke Math. J. 58 (1989), no. 2, 499-512 https://doi.org/10.1215/S0012-7094-89-05822-5 - J. McNeal, Local geometry of decoupled pseudoconvex domains, Complex analysis (Wuppertal, 1991), 223-230, Aspects Math., E17, Vieweg, Braunschweig, 1991
- J. McNeal, Estimates on the Bergman kernels of convex domains, Adv. Math. 109 (1994), no. 1, 108-139 https://doi.org/10.1006/aima.1994.1082
-
J. McNeal, Subelliptic estimates and scaling in the
$\partial$ -Neumann problem, Explorations in complex and Riemannian geometry, 197-217, Contemp. Math., 332, Amer. Math. Soc., Providence, RI, 2003 https://doi.org/10.1090/conm/332/05937 - J. Moser, Holomorphic equivalence and normal forms of hypersurfaces, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 2, Stanford Univ., Stanford, Calif., 1973), pp. 109-112. Amer. Math. Soc., Providence, R. I., 1975
- J. Moser, The holomorphic equivalence of real hypersurfaces, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), pp. 659-668, Acad. Sci. Fennica, Helsinki, 1980
-
J. Moser and S. Webster, Normal forms for real surfaces in
$C^2$ near complex tangents and hyperbolic surface transformations, Acta Math. 150 (1983), no. 3-4, 255-296 https://doi.org/10.1007/BF02392973 -
A. Nagel, J. P. Rosay, E. M. Stein, and S. Wainger, Estimates for the Bergman and Szego kernels in
$C^2$ , Ann. of Math. (2) 129 (1989), no. 1, 113-149 https://doi.org/10.2307/1971487 - R. Narasimhan, Several Complex Variables, University of Chicago Press, Chicago, IL, 1971
- L. Nirenberg, Lectures on linear partial differential equations, Amer. Math. Soc., Providence, RI, 1973
- S. Pinchuk, The scaling method and holomorphic mappings, Several complex variables and complex geometry, Part 1 (Santa Cruz, CA, 1989), 151-161, Proc. Sympos. Pure Math., 52, Part 1, Amer. Math. Soc., Providence, RI, 1991
-
J. P. Rosay, Sur une caracterisation de la boule parmi les domaines de
$C^n$ par son groupe d'automorphismes, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 4, ix, 91-97 https://doi.org/10.5802/aif.768 - R. Saerens and W. Zame, The isometry groups of manifolds and the automorphism groups of domains, Trans. Amer. Math. Soc. 301 (1987), no. 1, 413-429 https://doi.org/10.2307/2000347
- R. Schoen, On the conformal and CR automorphism groups, Geom. Funct. Anal. 5 (1995), no. 2, 464-481 https://doi.org/10.1007/BF01895676
- S. Sternberg, Local contractions and a theorem of Poincare, Amer. J. Math. 79 (1957), 809-824 https://doi.org/10.2307/2372437
- N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. (N.S.) 2 (1976), no. 1, 131-190 https://doi.org/10.4099/math1924.2.131
- S.Webster, On the Moser normal form at a non-umbilic point, Math. Ann. 233 (1978), no. 2, 97-102 https://doi.org/10.1007/BF01421918
- S.Webster, On the proof of Kuranishi's embedding theorem, Ann. Inst. H. Poincare Anal. Non Lineaire 6 (1989), no. 3, 183-207 https://doi.org/10.1016/S0294-1449(16)30322-5
- J. Winkelmann, Realizing connected Lie groups as automorphism groups of complex manifolds, Comment. Math. Helv. 79 (2004), no. 2, 285-299 https://doi.org/10.1007/s00014-003-0794-5
-
B. Wong, Characterization of the unit ball in
$C^n$ by its automorphism group, Invent. Math. 41 (1977), no. 3, 253-257 https://doi.org/10.1007/BF01403050 - H.Wu, Old and new invariant metrics on complex manifolds, Several complex variables (Stockholm, 1987/1988), 640-682, Math. Notes, 38, Princeton Univ. Press, Princeton, NJ, 1993
Cited by
- Complete prolongation for infinitesimal automorphisms on almost complex manifolds vol.264, pp.4, 2010, https://doi.org/10.1007/s00209-009-0496-9
- Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type vol.365, pp.3-4, 2016, https://doi.org/10.1007/s00208-015-1278-9
- Integrable Submanifolds in Almost Complex Manifolds vol.20, pp.1, 2010, https://doi.org/10.1007/s12220-009-9099-2
- The automorphism groups of domains in complex space: a survey vol.36, pp.2, 2013, https://doi.org/10.2989/16073606.2013.779982