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Heat kernel upper bounds on a complete non-compact manifold

  • Autores: Alexander Grigor'yan
  • Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 10, Nº 2, 1994, págs. 395-452
  • Idioma: inglés
  • Títulos paralelos:
    • Cotas superiores del núcleo del calor en variedades completas no-compactas
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  • Resumen
    • Let M be a smooth connected non-compact geodesically complete Riemannian manifold, ? denote the Laplace operator associated with the Riemannian metric, n = 2 be the dimension of M. Consider the heat equation on the manifold ut - ?u = 0, where u = u(x,t), x Î 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 ? +8 and r = dist(x,y) ? +8.

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