Título inglés | Heat kernel upper bounds on a complete non-compact manifold. |
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Título español | Cotas superiores del núcleo del calor en variedades completas no-compactas. |
Autor/es | Grigor'yan, Alexander |
Organización | Dep. Math. Univ. Bielefeld, Bielefeld, Alemania |
Revista | 0213-2230 |
Publicación | 1994, 10 (2): 395-452, 35 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | 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 manifold ut - Δu = 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 → +∞ and r ≡ dist(x,y) → +∞. |
Clasificación UNESCO | 121015 |
Palabras clave español | Kernel ; Acotación ; Variedades topológicas ; Límite superior |
Código MathReviews | MR1286481 |
Código Z-Math | Zbl 0810.58040 |
Acceso al artículo completo |