Journal
COMPOSITIO MATHEMATICA
Volume 149, Issue 11, Pages 1856-1870Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1112/S0010437X12000322
Keywords
Poincare-Lelong equation; Hodge-Laplacian heat equation; Kahler manifolds; Convex exhaustion
Categories
Funding
- NSF [DMS-1105549]
- Hong Kong RGC General Research Fund [CUHK 403011]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1105549] Funding Source: National Science Foundation
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In this paper, we develop a method of solving the Poincare-Lelong equation, mainly via the study of the large time asymptotics of a global solution to the Hodge-Laplace heat equation on (1, 1)-forms. The method is effective in proving an optimal result when M has nonnegative bisectional curvature. It also provides an alternate proof of a recent gap theorem of the first author.
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