Matrix Li–Yau–Hamilton estimates under Ricci flow and parabolic frequency-Reference-Cited by-同舟云学术

Matrix Li–Yau–Hamilton estimates under Ricci flow and parabolic frequency

Published:2024-02-26 Issue:3 Volume:63 Page:
ISSN:0944-2669
Container-title:Calculus of Variations and Partial Differential Equations
language:en
Short-container-title:Calc. Var.

Author:

Li Xiaolong^ORCID,Zhang Qi S.

Abstract

AbstractWe prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply these estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature.

Funder

Simons Foundation

Wichita State University

Directorate for Mathematical and Physical Sciences

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s00526-024-02668-x.pdf

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