A. Grigor’yan

activity

20102026

most citedExistence of positive solutions to some nonlinear equations on locally finite graphs

108 citations · 294 across the 20 of their papers we have counts for

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4 papers · 1 filter

math.DG2022

Asymptotic behavior of the heat semigroup on certain Riemannian manifolds

Alexander Grigor'yan, Effie Papageorgiou, Hong-Wei Zhang

We show that, on a complete, connected and non-compact Riemannian manifold of non-negative Ricci curvature, the solution to the heat equation with $L^{1}$ initial data behaves asym…

math.DG2022

Poincaré constant on manifolds with ends

Alexander Grigor'yan, Satoshi Ishiwata, Laurent Saloff-Coste

We obtain optimal estimates of the Poincaré constant of central balls on manifolds with finitely many ends. Surprisingly enough, the Poincaré constant is determined by the second l…

math.DG2022

Volume growth and on-diagonal heat kernel bounds on Riemannian manifolds with an end

Alexander Grigor'yan, Philipp Sürig

We investigate heat kernel estimates of the form $p_{t} (x, x) \geq c_{x} t^{- α},$ for large enough $t,$ where $α$ and $c_{x}$ are positive reals and $c_{x}$ may depend on $x,$ on man…

math.DG2020

Geometric analysis on manifolds with ends

Alexander Grigor'yan, Satoshi Ishiwata, Laurent Saloff-Coste

In this survey article, we discuss some recent progress on geometric analysis on manifold with ends. In the final section, we construct manifolds with ends with oscillating volume…