Gradient Estimates for the CR Heat Equation on Closed Sasakian Manifolds

In this paper, we obtain a CR version Li–Yau type gradient estimate for positive solutions of the CR heat equation on closed Sasakian manifolds. As its applications, we derive the Harnack inequality and upper bound estimate for the heat kernel. Finally, we obtain Perelman-type entropy formula for cl...

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Bibliographic Details
Published in:The Journal of geometric analysis 2024-08, Vol.34 (8), Article 239
Main Author: Zhao, Biqiang
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Manifolds
Mathematics
Mathematics and Statistics
Thermodynamics
Upper bounds
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Summary:In this paper, we obtain a CR version Li–Yau type gradient estimate for positive solutions of the CR heat equation on closed Sasakian manifolds. As its applications, we derive the Harnack inequality and upper bound estimate for the heat kernel. Finally, we obtain Perelman-type entropy formula for closed Sasakian manifolds.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-024-01681-y