| 摘要: |
| 本文主要研究了带有一般梯度项的非线性抛物方程的矩阵型Li-Yau-Hamilton估计.利用张量最大值原理证明了当Riemann度量沿Ricci流演化时Riemann流形上非线性抛物方程的矩阵型Li-Yau-Hamilton估计,其次证明了当Kähler度量沿Kähler-Ricci流演化时Kähler流形上非线性抛物方程的矩阵型Li-Yau-Hamilton估计.这些结果推广了梯度项为平方项时的相关结果. |
| 关键词: 非线性抛物方程 Li-Yau-Hamilton估计 Ricci流 Kähler-Ricci流 |
| DOI： |
| 分类号:O186.1 |
| 基金项目: |
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| MATRIX LI-YAU-HAMILTON ESTIMATES FOR NONLINEAR PARABOLIC EQUATIONS |
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CAO De-xia, REN Xin-an
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School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
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| Abstract: |
| In this paper we are concerned with the matrix Li-Yau-Hamilton estimates for nonlinear parabolic equations. By using the maximum principle for tensor, we derive such an estimate for nonlinear parabolic equations on Riemannian manifolds with metric evolving under the Ricci flow. Then we consider the estimate for nonlinear parabolic equations on Kähler manifolds with Kähler metrics evolving under the Kähler-Ricci flow. These results generalize the corresponding ones when the gradient term is quadratic. |
| Key words: nonlinear parabolic equation Li-Yau-Hamilton estimate Ricci flow KählerRicci flow |
