AbstractI am going to present an introduction into the geometric approach to Monge– Ampère operators and equations based on contact and symplectic structures of cotangent and the 1st jet bundles of a smooth manifold. This approach was developed by V. Lychagin and goes back to the ideas of E. Cartan and his successor T. Lepage. I shall try to make my talk self-contained. I also plan to discuss ...
In this talk, we discuss the global behaviors of the heat kernel and Green's function one the complete manifold with nonnegative Ricci curvature. we first obtain sharp two-side Gaussian bounds for the heat kernel that sharpens the well-known Li-Yau’s two-side bounds, based on the sharp Li-Yau’s Harnack inequality on such a manifold. As an application, we get the optimal gradient and Laplacian...
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