Constrained matrix Li-Yau-Hamilton estimates on Kähler manifolds

Ren, Xin-An; Yao, Sha; Shen, Li-Ju; Zhang, Guangying

doi:10.1007/s00208-014-1092-9

Cited by 4 publications

(2 citation statements)

References 24 publications

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“…Inspired by Chow’s interpolation consideration [ 14 ] of Li-Yau’s and Hamilton’s Harnack inequalities on a surface, Chow and Ni [ 56 , Theorem 2.2] proved that if is a complete solution to Kähler-Ricci flow with bounded nonnegative bisectional curvature and if u is a positive solution to the forward conjugate heat equation then The equality holds if and only if is an expanding Kähler-Ricci soliton. These results were generalized to the constrained case by Ren, Yao, Shen, and Zhang [ 62 ].…”

Section: Introductionmentioning

confidence: 99%

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

Li,

Zhang

2024

Calc. Var.

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We 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.

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Section: Introductionmentioning

confidence: 99%

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

Li,

Zhang

2024

Calc. Var.

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“…In [30], we extended the matrix Li-Yau-Hamilton estimates due to Cao-Ni and Chow-Ni on Kähler manifolds to the constrained case.…”

Section: Introductionmentioning

confidence: 99%

Matrix Li-Yau-Hamilton Estimates for Nonlinear Heat Equations

Ren

2019

Preprint

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In this paper we are concerned with the matrix Li-Yau-Hamilton estimates for nonlinear heat equations. Firstly, we derive such estimate on a Kähler manifold with a fixed Kähler metric. Then we consider the estimate on Kähler manifolds with Kähler metrics evolving under the rescaled Kähler-Ricci flow. Both of the estimates are generalized to constrained cases. Finally, we extend the estimtes to more general nonlinear heat equations on both Riemannian manifolds and Kähler manifolds.

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