ricci -调和流下热方程的Hamilton型梯度估计

IF 0.3 Q4 MATHEMATICS

Acta Mathematica Vietnamica Pub Date : 2025-05-22 DOI:10.1007/s40306-025-00570-y

Liang-Chu Chang, Nguyen Thac Dung, Chiung-Jue Anna Sung

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引用次数: 0

摘要

本文的目的是研究由里奇-谐波流演化的黎曼流形上的线性热方程。我们首先展示了热方程正解的Hamilton型梯度估计，这使我们能够推导出哈纳克不等式。值得注意的是，与Bailesteanu[1]的Li-Yau型估计相比，我们的梯度估计可以在不假设流中谐波量的情况下得到。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hamilton Type Gradient Estimates for a Heat Equation under the Ricci-harmonic Flow

Our aim in this paper is to study the linear heat equation on a Riemannian manifold evolving by the Ricci-harmonic flow. We first show a Hamilton type gradient estimate for the positive solution of the heat equation, which allows us to derive a Harnack inequality. It is worthy to note that comparing with the Li-Yau type estimate by Bailesteanu [1], our gradient estimate can be obtained without any assumption on the harmonic quantity in the flow.

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来源期刊

Acta Mathematica Vietnamica MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.