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http://dx.doi.org/10.4134/JKMS.2003.40.4.747

A VANISHING THEOREM FOR L2 COHOMOLOGY ON COMPLETE MANIFOLDS  

Mcneal, Jeffery-D. (Department of Mathematics Ohio State University)
Publication Information
Journal of the Korean Mathematical Society / v.40, no.4, 2003 , pp. 747-756 More about this Journal
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
Kaehler manifold; cohomology; vanishing theorems;
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  • Reference
1 On the L² cohomology groups of isolated singularities /
[ T.Ohsawa ] / Adv. Stud. Pure. Math., Math. Soc. Japan
2 /
[ R.O.Wells ] / Differential Analysis on Complex Manifolds
3 Weighted estimates for the <TEX>$\overline(\partial)$</TEX> equation /
[ B.Berndtsson ] / Complex Analysis and Geometry, Proceedings of a conference at Ohio State University
4 Kahler hyperbolicity and L²-Hodge theory /
[ M.Gromov ] / J. Diff. Geo.
5 A special Stoke's theorem for complete Riemannian manifolds /
[ M.Gaffney ] / Ann. Math.   DOI   ScienceOn
6 Multiplier ideal sheaves and Kahler-Einstein metrics of positive scalar curvature /
[ A.Nadel ] / Ann. Math.   DOI   ScienceOn
7 A remark on the completeness of the Bergman metric /
[ T.Ohsawa ] / Proc. Japan Acad. Sci.   DOI
8 Applications of L² estimates and some complex geometry /
[ T.Ohsawa ] / Geometric Complex Analysis
9 L² harmonic forms for a class of complete Kahler metrics /
[ E.Hunsicker ] / Mich. Math. J.   DOI
10 Hodge theory with degenerating coefficients. L² cohomology in the Poincare metric /
[ S.Zucker ] / Ann. Math.   DOI   ScienceOn
11 /
[ P.Griffths;J.Harris ] / Principles of algebraic geometry
12 logarithmic growth of the Bergman kernel ofr weakly pseudoconvex domains in C³ of finite type /
[ G.Herbort ] / Manuscripta Math.   DOI
13 L²-harmonic forms on complete Riemannian manifolds /
[ M.Anderson ] / Lecture Notes in Math.
14 Vanishing theorems for L²-cohomology on infinite coverings pf compact Kahler manifolds and applications in algebraic geometry /
[ J.Jost;Z.Zuo ] / Comm. Anal. Geo.   DOI
15 The zero-in-the-spectrum question /
[ J.Lott ] / L'Enseign. Math.
16 L² cohomology and index theorem for the Bergman metric /
[ H.Donnelly;C.Fefferman ] / Ann. Math.   DOI   ScienceOn
17 L² cohomology of the Bergman metric for weakly pseudoconvex domains /
[ H.Donnelly ] / Ill. Math. J.
18 Kahler parabolicity and the Euler number of compact manifolds of non-positive sectional curvature /
[ J.Cao;F.Xavier ] / Math. Ann.   DOI   ScienceOn
19 Spectral asymmetry and Riemannian geometry /
[ M.Atiyah;V.Patodi;I.Singer ] / Math. Proc. Cambridge Philos. Soc.   DOI
20 L² cohomology of pseudoconvex domains with complete Kahler metric /
[ H.Donnelly ] / Mich. Math. J.   DOI
21 L² harmonic forms on complete manifolds /
[ J.Dodziuk ] / Seminar on differential geometry, Ann. of Math. Stud.
22 L² harmonic forms on some complete Kahler manifolds /
[ J.D.McNeal ] / Math. Ann.   DOI   ScienceOn