A1 Journal article (refereed)
Sobolev and BV functions on RCD spaces via the short-time behavior of the heat kernel (2024)

Brena, C., Pasqualetto, E., & Pinamonti, A. (2024). Sobolev and BV functions on RCD spaces via the short-time behavior of the heat kernel. Communications in Contemporary Mathematics, Early online. https://doi.org/10.1142/S0219199725500026

JYU authors or editors

Publication details

All authors or editors: Brena, Camillo; Pasqualetto, Enrico; Pinamonti, Andrea

Journal or series: Communications in Contemporary Mathematics

ISSN: 0219-1997

eISSN: 1793-6683

Publication year: 2024

Publication date: 06/12/2024

Volume: Early online

Publisher: World Scientific

Publication country: Singapore

Publication language: English

DOI: https://doi.org/10.1142/S0219199725500026

Publication open access: Not open

Publication channel open access: 

Web address of parallel published publication (pre-print):  https://doi.org/10.48550/arXiv.2212.03910

Abstract

In the setting of finite-dimensional RCD(K,N) spaces, we characterize the p-Sobolev spaces for p∈(1,∞) and the space of functions of bounded variation in terms of the short-time behavior of the heat flow. Moreover, we prove that Cheeger p-energies and total variations can be computed as limits of nonlocal functionals involving the heat kernel.

Keywords: function analysis; differential geometry; metric spaces

Free keywords: Sobolev function; function of bounded variation; RCD space; heat kernel

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2024

Preliminary JUFO rating: 1