TY - JOUR
T1 - A probabilistic approach to the maximal diameter theorem
AU - Kuwada, Kazumasa
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013/3
Y1 - 2013/3
N2 - Under a positive curvature and a finite dimension in terms of the Bakry-Émery tensor on a Riemannian manifold, the Bonnet-Myers type diameter bound and the rigidity theorem are extended. The corresponding second order generator need not be symmetrizable. The proof is based on the Laplacian comparison theorem and stochastic analysis of radial processes.
AB - Under a positive curvature and a finite dimension in terms of the Bakry-Émery tensor on a Riemannian manifold, the Bonnet-Myers type diameter bound and the rigidity theorem are extended. The corresponding second order generator need not be symmetrizable. The proof is based on the Laplacian comparison theorem and stochastic analysis of radial processes.
KW - Bakry-Émery Ricci tensor
KW - Bonnet-Myers theorem
KW - Diffusion process
KW - Laplacian comparison theorem
KW - Maximal diameter theorem
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U2 - 10.1002/mana.201100330
DO - 10.1002/mana.201100330
M3 - Article
AN - SCOPUS:84874361026
SN - 0025-584X
VL - 286
SP - 374
EP - 378
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 4
ER -