Heat kernel estimates on connected sums of parabolic manifolds

Grigoryan A, Ishiwata S, Saloff-Coste L (2018)
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 113: 155-194.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor/in
Grigoryan, AlexanderUniBi; Ishiwata, Satoshi; Saloff-Coste, Laurent
Abstract / Bemerkung
We obtain matching two sided estimates of the heat kernel on a connected sum of parabolic manifolds, each of them satisfying the Li-Yau estimate. The key result is the on-diagonal upper bound of the heat kernel at a central point. Contrary to the non-parabolic case (which was settled in [15]), the on-diagonal behavior of the heat kernel in our case is determined by the end with the maximal volume growth function. As examples, we give explicit heat kernel bounds on the connected sums R-2#R-2 and R-1#R-2 where R-1 = R+ x S-1. (C) 2018 Elsevier Masson SAS. All rights reserved.
Stichworte
Heat kernel; Manifold with ends; Parabolic manifold; Integrated; resolvent
Erscheinungsjahr
2018
Zeitschriftentitel
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Band
113
Seite(n)
155-194
ISSN
0021-7824
eISSN
1776-3371
Page URI
https://pub.uni-bielefeld.de/record/2920323

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Grigoryan A, Ishiwata S, Saloff-Coste L. Heat kernel estimates on connected sums of parabolic manifolds. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES. 2018;113:155-194.
Grigoryan, A., Ishiwata, S., & Saloff-Coste, L. (2018). Heat kernel estimates on connected sums of parabolic manifolds. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 113, 155-194. doi:10.1016/j.matpur.2018.03.002
Grigoryan, A., Ishiwata, S., and Saloff-Coste, L. (2018). Heat kernel estimates on connected sums of parabolic manifolds. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 113, 155-194.
Grigoryan, A., Ishiwata, S., & Saloff-Coste, L., 2018. Heat kernel estimates on connected sums of parabolic manifolds. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 113, p 155-194.
A. Grigoryan, S. Ishiwata, and L. Saloff-Coste, “Heat kernel estimates on connected sums of parabolic manifolds”, JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, vol. 113, 2018, pp. 155-194.
Grigoryan, A., Ishiwata, S., Saloff-Coste, L.: Heat kernel estimates on connected sums of parabolic manifolds. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES. 113, 155-194 (2018).
Grigoryan, Alexander, Ishiwata, Satoshi, and Saloff-Coste, Laurent. “Heat kernel estimates on connected sums of parabolic manifolds”. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 113 (2018): 155-194.