A Varadhan type estimate on manifolds with time-dependent metrics and constant volume

作者：Abdallah Hiba^*

来源：Journal de Mathematiques Pures et Appliquees, 2013, 99(4): 409-418.

DOI：10.1016/j.matpur.2012.09.007

• Laplacian
• Fundamental solution
• Parametrix
• Riemannian metric

In this paper, we consider a compact n-dimensional manifold M with a time-dependent smooth Riemannian metric g(t) whose volume is constant in t. We give a suitable form of the fundamental solution of the linear parabolic operator Delta(g(t)) - partial derivative/partial derivative t, where Delta(g(t)) stands for the time-dependent Laplacian based on g(t). We focus on the short-time behavior of the given fundamental solution, extending Varadhan's estimate which holds in the case where the metric is fixed.

• 出版日期2013-4