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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