积分曲率条件下热方程的椭圆型梯度估计

王建红

数学学报 ›› 2022, Vol. 65 ›› Issue (5) : 763-774.

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PDF(492 KB)
数学学报 ›› 2022, Vol. 65 ›› Issue (5) : 763-774. DOI: 10.12386/A20210040
论文

积分曲率条件下热方程的椭圆型梯度估计

    王建红
作者信息 +

Elliptic Gradient Estimate for Heat Equation with Integral Ricci Curvature Condition

    Jian Hong WANG
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文章历史 +

摘要

本文得到了在紧黎曼流形上,当Ricci曲率的积分有界时热方程正解的一种椭圆型梯度估计,证明了一种新的积分曲率条件下的体积比较定理,改进了Petersen-Wei的关于积分曲率的体积比较定理.

Abstract

The main purpose of this paper is to establish the elliptic gradient estimate for the heat equation on compact Riemannian manifold with control on integral Ricci curvature. We also derived the volume comparison theorem under the new integral Ricci curvature condition which extended Petersen-Wei's volume comparison theorem.

关键词

热方程 / 椭圆型梯度估计 / Ricci曲率积分 / 体积比较定理

Key words

heat equation / elliptic gradient estimate / integral Ricci curvature / volume comparison theorem

引用本文

导出引用
王建红. 积分曲率条件下热方程的椭圆型梯度估计. 数学学报, 2022, 65(5): 763-774 https://doi.org/10.12386/A20210040
Jian Hong WANG. Elliptic Gradient Estimate for Heat Equation with Integral Ricci Curvature Condition. Acta Mathematica Sinica, Chinese Series, 2022, 65(5): 763-774 https://doi.org/10.12386/A20210040

参考文献

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