DOI QR코드

DOI QR Code

A VANISHING THEOREM FOR L2 COHOMOLOGY ON COMPLETE MANIFOLDS

  • Mcneal, Jeffery-D. (Department of Mathematics Ohio State University)
  • Published : 2003.07.01

Abstract

We establish a vanishing theorem on the square-integrable cohomology associated to the Cauchy-Riemann complex on some complete Kaehler manifolds. The hypothesis needed for this result is a growth condition on a primitive of the Kaehler form.

Keywords

References

  1. Lecture Notes in Math. v.1339 L²-harmonic forms on complete Riemannian manifolds M.Anderson
  2. Math. Proc. Cambridge Philos. Soc. v.77 Spectral asymmetry and Riemannian geometry M.Atiyah;V.Patodi;I.Singer https://doi.org/10.1017/S0305004100049410
  3. Complex Analysis and Geometry, Proceedings of a conference at Ohio State University v.9 Weighted estimates for the $\overline(\partial)$ equation B.Berndtsson
  4. Math. Ann. v.319 Kahler parabolicity and the Euler number of compact manifolds of non-positive sectional curvature J.Cao;F.Xavier https://doi.org/10.1007/PL00004444
  5. Seminar on differential geometry, Ann. of Math. Stud. v.102 L² harmonic forms on complete manifolds J.Dodziuk
  6. Mich. Math. J. v.41 L² cohomology of pseudoconvex domains with complete Kahler metric H.Donnelly https://doi.org/10.1307/mmj/1029005071
  7. Ill. Math. J. v.41 L² cohomology of the Bergman metric for weakly pseudoconvex domains H.Donnelly
  8. Ann. Math. v.118 L² cohomology and index theorem for the Bergman metric H.Donnelly;C.Fefferman https://doi.org/10.2307/2006983
  9. Ann. Math. v.60 A special Stoke's theorem for complete Riemannian manifolds M.Gaffney https://doi.org/10.2307/1969703
  10. Principles of algebraic geometry P.Griffths;J.Harris
  11. J. Diff. Geo. v.33 Kahler hyperbolicity and L²-Hodge theory M.Gromov
  12. Manuscripta Math. v.45 logarithmic growth of the Bergman kernel ofr weakly pseudoconvex domains in C³ of finite type G.Herbort https://doi.org/10.1007/BF01168581
  13. Mich. Math. J. v.50 L² harmonic forms for a class of complete Kahler metrics E.Hunsicker https://doi.org/10.1307/mmj/1028575737
  14. Comm. Anal. Geo. v.8 Vanishing theorems for L²-cohomology on infinite coverings pf compact Kahler manifolds and applications in algebraic geometry J.Jost;Z.Zuo https://doi.org/10.4310/CAG.2000.v8.n1.a1
  15. L'Enseign. Math. v.42 The zero-in-the-spectrum question J.Lott
  16. Math. Ann. v.323 L² harmonic forms on some complete Kahler manifolds J.D.McNeal https://doi.org/10.1007/s002080100305
  17. Ann. Math. v.132 Multiplier ideal sheaves and Kahler-Einstein metrics of positive scalar curvature A.Nadel https://doi.org/10.2307/1971429
  18. Proc. Japan Acad. Sci. v.57 A remark on the completeness of the Bergman metric T.Ohsawa https://doi.org/10.3792/pjaa.57.238
  19. Adv. Stud. Pure. Math., Math. Soc. Japan v.22 On the L² cohomology groups of isolated singularities T.Ohsawa
  20. Geometric Complex Analysis Applications of L² estimates and some complex geometry T.Ohsawa
  21. Differential Analysis on Complex Manifolds R.O.Wells
  22. Ann. Math. v.109 Hodge theory with degenerating coefficients. L² cohomology in the Poincare metric S.Zucker https://doi.org/10.2307/1971221