Thermonuclear On Manifold And Its Application

In this paper we make a comprehensive summarization about heat kernel and its application. We give detailed descriptions of the properties of heat kernel. When it comes to the application of heat kernel, we present two parts. One is the application in the estimate of eigenvalues, the other is that by embedding Riemannian Manifolds by their heat kernel, we get a precompactness theorem. In the end, we give a brief introduction of the latest development of the application of heat kernel in the engineering fields.