# Heat kernel upper bounds on a complete non-compact manifold.

Revista Matemática Iberoamericana (1994)

- Volume: 10, Issue: 2, page 395-452
- ISSN: 0213-2230

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topGrigor'yan, Alexander. "Heat kernel upper bounds on a complete non-compact manifold.." Revista Matemática Iberoamericana 10.2 (1994): 395-452. <http://eudml.org/doc/39447>.

@article{Grigoryan1994,

abstract = {Let M be a smooth connected non-compact geodesically complete Riemannian manifold, Δ denote the Laplace operator associated with the Riemannian metric, n ≥ 2 be the dimension of M. Consider the heat equation on the manifoldut - Δu = 0,where u = u(x,t), x ∈ M, t > 0. The heat kernel p(x,y,t) is by definition the smallest positive fundamental solution to the heat equation which exists on any manifold (see [Ch], [D]). The purpose of the present work is to obtain uniform upper bounds of p(x,y,t) which would clarify the behaviour of the heat kernel as t → +∞ and r ≡ dist(x,y) → +∞.},

author = {Grigor'yan, Alexander},

journal = {Revista Matemática Iberoamericana},

keywords = {Kernel; Acotación; Variedades topológicas; Límite superior; heat kernel; isoperimetric inequalities; spectral geometry},

language = {eng},

number = {2},

pages = {395-452},

title = {Heat kernel upper bounds on a complete non-compact manifold.},

url = {http://eudml.org/doc/39447},

volume = {10},

year = {1994},

}

TY - JOUR

AU - Grigor'yan, Alexander

TI - Heat kernel upper bounds on a complete non-compact manifold.

JO - Revista Matemática Iberoamericana

PY - 1994

VL - 10

IS - 2

SP - 395

EP - 452

AB - Let M be a smooth connected non-compact geodesically complete Riemannian manifold, Δ denote the Laplace operator associated with the Riemannian metric, n ≥ 2 be the dimension of M. Consider the heat equation on the manifoldut - Δu = 0,where u = u(x,t), x ∈ M, t > 0. The heat kernel p(x,y,t) is by definition the smallest positive fundamental solution to the heat equation which exists on any manifold (see [Ch], [D]). The purpose of the present work is to obtain uniform upper bounds of p(x,y,t) which would clarify the behaviour of the heat kernel as t → +∞ and r ≡ dist(x,y) → +∞.

LA - eng

KW - Kernel; Acotación; Variedades topológicas; Límite superior; heat kernel; isoperimetric inequalities; spectral geometry

UR - http://eudml.org/doc/39447

ER -

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