非线性抛物方程的矩阵型Li-Yau-Hamilton估计OA

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.