DOI QR코드

DOI QR Code

L2 조화미분형식과 극소초평면에의 응용

  • 윤갑진 (명지대학교 이과대학 수학과)
  • Published : 2002.04.01

Abstract

본 요약논문에서는 리만다양체에서 정의되는 L$^2$조화미분 형식의 성질과 존재성에 대하여 알아보고 그 응용으로 유클리드 공간의 극소초평에서 L$^2$조화미분형식과 위상구조와의 관계를 살펴본다.

Keywords

References

  1. Bull. of AMS v.13 no.2 Lº harmonic forms and a conjecture of Dodziuk-Singer M.T. Anderson https://doi.org/10.1090/S0273-0979-1985-15405-9
  2. The compactification of a minimal submanifold in Euclidean space by the Gauss map(Preprint)
  3. Societe Mathematique de France Asterisque v.32 no.33 Elliptic Operators,Discrete Groups and Von Neumann Algebras M.F. Atiyah
  4. Pitman Monographs Surveys Pure Appl. Math. v.52 Remarques sur l'equation de J. Simons, Differential Geometry (A symosium in honor of M. DoCarmo on his 60th birthday) P. Berard
  5. Ann. of Mathematics Studies v.103 Seminar on Minimal Submanifolds E. Bombieri(edt)
  6. Math. Res. Lett. v.4 The structure of stable minimal hypersurfaces in Rⁿ+¹ H-D Cao;Y. Shen;S. Zhu https://doi.org/10.4310/MRL.1997.v4.n5.a2
  7. Topology v.25 L₂-cohomology and group cohomology J. Cheeger;M. Gromov https://doi.org/10.1016/0040-9383(86)90039-X
  8. Courant Lecture Notes v.4 Miniaml surfaces T.H. Colding;W.P. MinicozziⅡ
  9. Bull. of AMS v.1 Stable complete minimal surfaces in R³ are planes M. DoCarmo;C.K. Peng https://doi.org/10.1090/S0273-0979-1979-14689-5
  10. Seminar on Differential Geometry v.102 Lº harmonic forms on complete manifolds J. Dodziuk
  11. Topology v.16 De Rham-Hodeg theory for Lº-cohomology of infinite coverings https://doi.org/10.1016/0040-9383(77)90013-1
  12. Proc. of AMS v.77 Lº harmonic forms on rotationally symmetric Riemannian manifolds https://doi.org/10.2307/2042193
  13. Varietes differentiables, forms, conrantes, formes harmoniques(2nd, ed.) no.122a G. DeRham
  14. Amer. J. Math. v.106 On the differential form spectrum of negatively curved Riemannian manifolds H. Donnely;F. Xavier https://doi.org/10.2307/2374434
  15. Comm. Pure and Appl. Math. v.33 The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature D. Fischer-Colbrie;R. Schoen https://doi.org/10.1002/cpa.3160330206
  16. Ann. of Math. v.60 A spectial Stokes theorem for Riemannian manifolds M. Gaffney https://doi.org/10.2307/1969703
  17. J. Diff. Geom. v.33 Kahler hyperbolicity and L₂-Hodge theory M. Gromov https://doi.org/10.4310/jdg/1214446039
  18. Comm. Pure Appl. Math. v.27 Sobolev and Iosperimetirc inequalities for Reimannian submanifolds D. Hoffman;J. Spruck https://doi.org/10.1002/cpa.3160270601
  19. Lectures on Minimal Submanifolds H.B. Lawson
  20. Research Institute of Mathematics no.6 Lecture Notes in Deometric Analysis P. Li
  21. Curvature and Function Theory on Reimannian Manifolds(Preprint)
  22. GAFA(Geometric And Functional Analysis) v.7 Lº cohomology of geometrically infinite hyperbolic 3-manifolds J. Lott https://doi.org/10.1007/PL00001617
  23. Geometry and Global Analysis (Sendai 1993) Harmonic 1-forms on a complete stable minimal hypersurfaces R. Miyaoka
  24. A Survey of Manimal Surfaces R. Osserman
  25. Comm. Math. Helv. v.51 Harmonic maps and the topology of stable hypersurfaces and manifolds of nonnegative Ricci curvature R. Schoen;S-T. Yau https://doi.org/10.1007/BF02568161
  26. Conference Proceedings and Lecture Notes in Geometry and Topology v.1 Lectures on Defferential Geometry
  27. Amer. Jour. of Math. v.120 On stable minimal hypersurfaces in Rⁿ+¹ Y-B. Shen;X-H. Zhu https://doi.org/10.1353/ajm.1998.0005
  28. Ann. of Math. v.88 Minimal varieties in Riemannian manifolds J. Simons https://doi.org/10.2307/1970556
  29. Jour. of Math. Soc. Japan v.48 Lº harmonic forms and stability of minimal hypersurfaces S. Tanno https://doi.org/10.2969/jmsj/04840761
  30. Foundations of differentiable manifolds and Lie groups F.W. Warner
  31. The Bochner Technique in Differential Geometry(Preprint) H. Wu
  32. will appear in Geometriae Dedicata Total scalar curvature and Lº harmonic one forms on a miniaml hypersurface in Enclidean space G. Yun