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Isoperimetric constants, the geometry of ends, and large time heat diffusion in Riemannian manifolds. (English) Zbl 0723.58048

The aim of this paper is to present geometric informations about a non- compact Riemannian manifold M of dimension \(n\geq 2\), which are obtained from inequalities of the form \(p(x,y,t)\leq const._{\nu}t^{-\nu /2}>0\) where p(x,y,t) (x,y\(\in M\), \(t>0)\) is the minimal positive heat kernel corresponding to the Laplace-Beltrami operator \(\Delta\) acting on functions on M.

MSC:

58J35 Heat and other parabolic equation methods for PDEs on manifolds
58J65 Diffusion processes and stochastic analysis on manifolds
35K05 Heat equation
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