Tamed spaces-Dirichlet spaces with distribution-valued Ricci bounds

Erbar M, Rigoni C, Sturm K-T, Tamanini L (2022)
Journal de Mathématiques Pures et Appliquées 161: 1-69.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Erbar, MatthiasUniBi; Rigoni, Chiara; Sturm, Karl-Theodor; Tamanini, Luca
Abstract / Bemerkung
We develop the theory of tamed spaces which are Dirichlet spaces with distribution-valued lower bounds on the Ricci curvature and investigate these from an Eulerian point of view. To this end we analyze in detail singular perturbations of Dirichlet form by a broad class of distributions. The distributional Ricci bound is then formulated in terms of an integrated version of the Bochner inequality using the perturbed energy form and generalizing the well-known Bakry-Emery curvature-dimension condition. Among other things we show the equivalence of distributional Ricci bounds to gradient estimates for the heat semigroup in terms of the Feynman-Kac semigroup induced by the taming distribution as well as consequences in terms of functional inequalities. We give many examples of tamed spaces including in particular Riemannian manifolds with interior singularities and singular boundary behavior. (c) 2022 Elsevier Masson SAS. All rights reserved.
Stichworte
Ricci curvature; Metric measure space; Distribution; Dirichlet form
Erscheinungsjahr
2022
Zeitschriftentitel
Journal de Mathématiques Pures et Appliquées
Band
161
Seite(n)
1-69
ISSN
0021-7824
eISSN
1776-3371
Page URI
https://pub.uni-bielefeld.de/record/2963458

Zitieren

Erbar M, Rigoni C, Sturm K-T, Tamanini L. Tamed spaces-Dirichlet spaces with distribution-valued Ricci bounds. Journal de Mathématiques Pures et Appliquées. 2022;161:1-69.
Erbar, M., Rigoni, C., Sturm, K. - T., & Tamanini, L. (2022). Tamed spaces-Dirichlet spaces with distribution-valued Ricci bounds. Journal de Mathématiques Pures et Appliquées, 161, 1-69. https://doi.org/10.1016/j.matpur.2022.02.002
Erbar, M., Rigoni, C., Sturm, K. - T., and Tamanini, L. (2022). Tamed spaces-Dirichlet spaces with distribution-valued Ricci bounds. Journal de Mathématiques Pures et Appliquées 161, 1-69.
Erbar, M., et al., 2022. Tamed spaces-Dirichlet spaces with distribution-valued Ricci bounds. Journal de Mathématiques Pures et Appliquées, 161, p 1-69.
M. Erbar, et al., “Tamed spaces-Dirichlet spaces with distribution-valued Ricci bounds”, Journal de Mathématiques Pures et Appliquées, vol. 161, 2022, pp. 1-69.
Erbar, M., Rigoni, C., Sturm, K.-T., Tamanini, L.: Tamed spaces-Dirichlet spaces with distribution-valued Ricci bounds. Journal de Mathématiques Pures et Appliquées. 161, 1-69 (2022).
Erbar, Matthias, Rigoni, Chiara, Sturm, Karl-Theodor, and Tamanini, Luca. “Tamed spaces-Dirichlet spaces with distribution-valued Ricci bounds”. Journal de Mathématiques Pures et Appliquées 161 (2022): 1-69.

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