Super Ricci flows for weighted graphs

Erbar M, Kopfer E (2020)
JOURNAL OF FUNCTIONAL ANALYSIS 279(6): UNSP 108607.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Erbar, MatthiasUniBi; Kopfer, Eva
Abstract / Bemerkung
We present a notion of super Ricci flow for time-dependent finite weighted graphs. A challenging feature is that these flows typically encounter singularities where the underlying graph structure changes. Our notion is robust enough to allow the flow to continue past these singularities. As a crucial tool for this purpose we study the heat flow on such singular time-dependent weighted graphs with changing graph structure. We then give several equivalent characterizations of super Ricci flows in terms of a discrete dynamic Bochner inequality, gradient and transport estimates for the heat flow, and dynamic convexity of the entropy along discrete optimal transport paths. The latter property can be used to show that our notion of super Ricci flow is consistent with classical super Ricci flows for manifolds (or metric measure spaces) in a discrete to continuum limit. (C) 2020 Elsevier Inc. All rights reserved.
Stichworte
Ricci flow; Graph; Optimal transport; Entropy
Erscheinungsjahr
2020
Zeitschriftentitel
JOURNAL OF FUNCTIONAL ANALYSIS
Band
279
Ausgabe
6
Art.-Nr.
UNSP 108607
ISSN
0022-1236
eISSN
1096-0783
Page URI
https://pub.uni-bielefeld.de/record/2944500

Zitieren

Erbar M, Kopfer E. Super Ricci flows for weighted graphs. JOURNAL OF FUNCTIONAL ANALYSIS. 2020;279(6): UNSP 108607.
Erbar, M., & Kopfer, E. (2020). Super Ricci flows for weighted graphs. JOURNAL OF FUNCTIONAL ANALYSIS, 279(6), UNSP 108607. doi:10.1016/j.jfa.2020.108607
Erbar, M., and Kopfer, E. (2020). Super Ricci flows for weighted graphs. JOURNAL OF FUNCTIONAL ANALYSIS 279:UNSP 108607.
Erbar, M., & Kopfer, E., 2020. Super Ricci flows for weighted graphs. JOURNAL OF FUNCTIONAL ANALYSIS, 279(6): UNSP 108607.
M. Erbar and E. Kopfer, “Super Ricci flows for weighted graphs”, JOURNAL OF FUNCTIONAL ANALYSIS, vol. 279, 2020, : UNSP 108607.
Erbar, M., Kopfer, E.: Super Ricci flows for weighted graphs. JOURNAL OF FUNCTIONAL ANALYSIS. 279, : UNSP 108607 (2020).
Erbar, Matthias, and Kopfer, Eva. “Super Ricci flows for weighted graphs”. JOURNAL OF FUNCTIONAL ANALYSIS 279.6 (2020): UNSP 108607.

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