108 citations · 294 across the 20 of their papers we have counts for
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Heat kernel estimates on connected sums of parabolic manifolds
Alexander Grigor'yan, Satoshi Ishiwata, Laurent Saloff-Coste
We obtain matching two sided estimates of the heat kernel on a connected sum of parabolic manifolds, each of them satisfying the Li-Yau estimate. The key result is the on-diagonal…
Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula
Alexander Grigor'yan, Naotaka Kajino
We prove that for a general diffusion process, certain assumptions on its behavior \emph{only within a fixed open subset} of the state space imply the existence and sub-Gaussian ty…
Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities
Alexander Grigor'yan, Shunxiang Ouyang, Michael Röckner
We prove upper and lower bounds of the heat kernel for the operator in $\mathbb{R}^{n}\setminus\{0} $ where . We obtain these bounds…
Two-sided estimates of heat kernels on metric measure spaces
Alexander Grigor'yan, Andras Telcs
We prove equivalent conditions for two-sided sub-Gaussian estimates of heat kernels on metric measure spaces.