Yamabe流下黎曼流形上热方程的梯度估计

Gradient Estimate for the Heat Equation on Riemannian Manifolds under the Yamabe Flow

研究了在Yamabe流下演化的一个完备非紧黎曼流形,对流形上热方程的正解给出了两种局部的梯度估计.作为应用,可以得到这个热方程的Harnack不等式.

The authors study a complete noncompact Riemannian manifold evolving under the Yamabe flow and derive two versions of localized gradient estimates for positive solutions to the heat equation on the evolving manifold. As an application, the Harnack inequality for the heat equation can be established immediately.