Heat Kernel Estimates on a Connected Sum of Two Copies of Rn Along a Surface of Revolution
作者: Alexer Grigor’yan Satoshi Ishiwata
刊名: Global and Stochastic Analysis, 2015, Vol.2 (1)
来源数据库: Mind Reader Publications
关键词: heat kernelconnected sumRiemannian manifolddiffusion processhitting probability
原始语种摘要: We prove sharp two sided heat kernel estimates on a connected sum of two copies of Rn along a surface of revolution taking into account a bottleneck effect. In the proof, estimates of the hitting probability of a non-compact set play a crucial role. For the heat kernel upper bound, we use isoperimetric inequalities on connected sums. For the heat kernel lower bound, we use a lower bound of the Dirichlet heat kernel in the exterior of a non-compact set.
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  • kernel 
  • bottleneck 瓶颈
  • estimates 估值
  • isoperimetric 等周的
  • bound 
  • compact 紧的
  • crucial 有决定性的
  • revolution 变革
  • account 计算
  • prove 实验