Matrix Li–Yau–Hamilton estimates under Kähler–Ricci flow
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Authors
Li, Xiaolong
Liu, Hao-Yue
Ren, Xin-An
Advisors
Issue Date
2025-02-28
Type
Article
Keywords
Heat equation , Kähler–Ricci flow , Li–Yau–Hamilton estimates , Matrix Harnack inequality
Citation
Li, X., Liu, HY. & Ren, XA. Matrix Li–Yau–Hamilton Estimates Under Kähler–Ricci Flow. J Geom Anal 35, 113 (2025). https://doi.org/10.1007/s12220-025-01948-y
Abstract
We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Kähler–Ricci flow. These estimates are further extended to the constrained setting. As an application, we obtain a monotonicity formula. © Mathematica Josephina, Inc. 2025.
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Publisher
Springer
Journal
Journal of Geometric Analysis
Book Title
Series
PubMed ID
ISSN
10506926