Zobrazeno 1 - 10
of 200
pro vyhledávání: '"GRIGOR'YAN, ALEXANDER"'
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 ingredients. (I) We have observed that the product rule does work for
Externí odkaz:
http://arxiv.org/abs/2406.09814
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 asymptotically as the mass times the heat kernel. In contrast to the previ
Externí odkaz:
http://arxiv.org/abs/2205.06105
We obtain optimal estimates of the Poincar\'e constant of central balls on manifolds with finitely many ends. Surprisingly enough, the Poincar\'e constant is determined by the second largest end. The proof is based on the argument by Kusuoka-Stroock
Externí odkaz:
http://arxiv.org/abs/2205.06100
Autor:
Grigor'yan, Alexander, Sürig, Philipp
We investigate heat kernel estimates of the form $p_{t}(x, x)\geq c_{x}t^{-\alpha},$ for large enough $t,$ where $\alpha$ and $c_{x}$ are positive reals and $c_{x}$ may depend on $x,$ on manifolds having at least one end.
Comment: 30 pages
Comment: 30 pages
Externí odkaz:
http://arxiv.org/abs/2201.05695
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-Yau2013, Grigoryan-Lin-Muranov-Yau2014, Grigoryan-Lin-Muranov-Yau2015
Externí odkaz:
http://arxiv.org/abs/2012.07302
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 functions which may turn out to have a different heat kernel estimates
Externí odkaz:
http://arxiv.org/abs/2007.15834
The goal of this paper is the spectral analysis of the Schr\"{o}dinger type operator $H=L+V$, the perturbation of the Taibleson-Vladimirov multiplier $L=\mathfrak{D}^{\alpha}$ by a potential $V$. Assuming that $V$ belongs to a certain class of potent
Externí odkaz:
http://arxiv.org/abs/2006.02263
The goal of this paper is twofold. We prove that the operator $H=L+V$ , a perturbation of the Taibleson-Vladimirov multiplier $L=\mathfrak{D}^{\alpha}$ by a potential $V(x)=b\left\Vert x\right\Vert ^{-\alpha},$ $b\geq b_{\ast},$ is essentially self-a
Externí odkaz:
http://arxiv.org/abs/2006.01821