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Sharp differential estimates of Li-Yau-Hamilton type for positive (p, p)-forms on Kähler manifolds (2011)
| Venue: | COMMUN. PURE APPL. MATH |
| Citations: | 1 - 1 self |
BibTeX
@ARTICLE{Ni11sharpdifferential,
author = {Lei Ni and Yanyan Niu},
title = { Sharp differential estimates of Li-Yau-Hamilton type for positive (p, p)-forms on Kähler manifolds},
journal = {COMMUN. PURE APPL. MATH},
year = {2011}
}
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Abstract
In this paper we study the heat equation (of Hodge Laplacian) deformation of.p; p/-forms on a Kähler manifold. After identifying the condition and establishing that the positivity of a.p; p/-form solution is preserved under such an invariant condition, we prove the sharp differential Harnack (in the sense of Li-Yau-Hamilton) estimates for the positive solutions of the Hodge Laplacian heat equation. We also prove a nonlinear version coupled with the Kähler-Ricci flow and some interpolating matrix differential Harnack-type estimates for both the Kähler-Ricci flow and the Ricci flow.
Keyphrases
hler manifold sharp differential estimate li-yau-hamilton type hler-ricci flow ricci flow nonlinear version interpolating matrix differential harnack-type estimate sharp differential harnack positive solution wiley periodical hodge laplacian heat equation invariant condition heat equation hodge laplacian
