Journal article

Rectifiability of the reduced boundary for sets of finite perimeter over RCD(K,N) spaces

Abstract:: This paper is devoted to the study of sets of finite perimeter in RCD(K,N) metric measure spaces. Its aim is to complete the picture of the generalization of De Giorgi’s theorem within this framework. Starting from the results of Ambrosio et al. (2019) we obtain uniqueness of tangents and rectifiability for the reduced boundary of sets of finite perimeter. As an intermediate tool, of independent interest, we develop a Gauss–Green integration-by-parts formula tailored to this setting. These results are new and non-trivial even in the setting of Ricci limits.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Bruè, E., Pasqualetto, E., & Semola, D. (2022). Rectifiability of the reduced boundary for sets of finite perimeter over RCD(K,N) spaces. Journal of the European Mathematical Society, 25(2), 413–465.

MLA Style

Bruè, E., et al. “Rectifiability of the Reduced Boundary for Sets of Finite Perimeter over RCD(K,N) Spaces.” Journal of the European Mathematical Society, vol. 25, no. 2, EMS Press , 2022, pp. 413–65.

Chicago Style

Bruè, E, E Pasqualetto, and D Semola. 2022. “Rectifiability of the Reduced Boundary for Sets of Finite Perimeter over RCD(K,N) Spaces.” Journal of the European Mathematical Society 25 (2): 413–65.
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Files:: Brue_et_al_2022_Rectifiability_of_the.pdf

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Publisher copy:: 10.4171/JEMS/1217

Authors

+ Bruè, E More by this author

Role:: Author

+ Pasqualetto, E More by this author

Role:: Author

+ Semola, D More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

Publisher:: EMS Press
Journal:: Journal of the European Mathematical Society More from this journal
Volume:: 25
Issue:: 2
Pages:: 413-465
Publication date:: 2022-02-15
Acceptance date:: 2021-12-27
DOI:: 10.4171/JEMS/1217
EISSN:: 1435-9863
ISSN:: 1435-9855

Language:: English
Keywords:: Gauss–Green formula

tangent cone

RCD space

set of finite perimeter

FFR

rectifiability
Pubs id:: 1226872
Local pid:: pubs:1226872
Deposit date:: 2021-12-28

Terms of use

Copyright holder:: European Mathematical Society
Copyright date:: 2022
Rights statement:: © 2022 European Mathematical Society. Published by EMS Press and licensed under a CC BY 4.0 license

Licence:: CC Attribution (CC BY)

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