Ricci流下方程解的梯度估计和Harnack不等式

发布时间：2018-06-02 18:45

  本文选题：Ricci流 + 热方程　； 参考：《中国科学技术大学》2017年博士论文

【摘要】：本文主要研究Ricci流下几类非线性抛物方程正解的梯度估计以及Harnack不等式。主要研究内容包括:(1)将Li-Yau对流形上热方程的梯度估计推广到Ricci流下非线性抛物方程,并建立相关的Harnack不等式;(2)沿Ricci流下,将Li-Yau估计中的常数α推广到满足一定系统的函数α(t);(3)作为满足一定系统的特殊情形,我们给出Li-Yau型,Hamilton型,等梯度估计。(4)研究了黎曼流形上非线性抛物方程,当α ≤ 0和α ≥ 1时,证明了 Hamilton椭圆型梯度估计和Liouville型定理,补充了 Zhu对0α1的结果。另外,导出了 Li-Yau型梯度估计和Harnack不等式,进而将Li和Xu的结果推广到非线性抛物方程。(5)研究了黎曼流形上介质穿透型方程的Hamilton型梯度估计和Liouville型定理,从而进一步简化了 Souplet和Zhang关于热方程的结果。
[Abstract]:In this paper, the gradient estimation and Harnack inequality of positive solutions for some nonlinear parabolic equations under Ricci flow are studied. The main research contents include: (1) the gradient estimation of the thermal equation on the Li-Yau convection is extended to the nonlinear parabolic equation under the Ricci flow, and the related Harnack inequality is established. In this paper, the constant 伪 in Li-Yau estimator is extended to the function 伪 t 3 of a certain system. As a special case of satisfying a certain system, we give the Li-Yau type Hamiltonian type and equal gradient estimator .4) We study the nonlinear parabolic equations on Riemannian manifolds. When 伪 鈮，

本文编号：1969800