108 citations · 294 across the 20 of their papers we have counts for
23 papers
Sharp long distance upper bounds for solutions of Leibenson's equation on Riemannian manifolds
Alexander Grigor'yan, Jin Sun, Philipp Sürig
We consider on Riemannian manifolds the Leibenson equation that is also known as a doubly nonlinear evolution equation. We prove sharp upper estimates o…
Eigenvalues of the Hodge Laplacian on digraphs
Alexander Grigor'yan, Yong Lin, S. -T. Yau +1
This paper aims to compute and estimate the eigenvalues of the Hodge Laplacians on directed graphs. We have devised a new method for computing Hodge spectra with the following two…
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 initial data behaves asym…
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…
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 for large enough where and are positive reals and may depend on on man…
Torsion of digraphs and path complexes
Alexander Grigor'yan, Yong Lin, Shing-Tung Yau
We define the notions of Reidemeister torsion and analytic torsion for directed graphs by means of the path homology theory introduced by the authors in \cite{Grigoryan-Lin-Muranov…