Monotonicity Formulas for Harmonic Functions in RCD(0,N) Spaces
Year of publication
2023
Authors
Gigli, Nicola; Violo, Ivan Yuri
Abstract
We generalize to the RCD(0,N) setting a family of monotonicity formulas by Colding and Minicozzi for positive harmonic functions in Riemannian manifolds with nonnegative Ricci curvature. Rigidity and almost rigidity statements are also proven, the second appearing to be new even in the smooth setting. Motivated by the recent work in Agostiniani et al. (Invent. Math. 222(3):1033–1101, 2020), we also introduce the notion of electrostatic potential in RCD spaces, which also satisfies our monotonicity formulas. Our arguments are mainly based on new estimates for harmonic functions in RCD(K,N) spaces and on a new functional version of the ‘(almost) outer volume cone implies (almost) outer metric cone’ theorem.
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Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Journal
Publisher
Volume
33
Issue
3
Article number
100
ISSN
Publication forum
Publication forum level
2
Open access
Open access in the publisher’s service
Yes
Open access of publication channel
Partially open publication channel
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object]
Publication country
United States
Internationality of the publisher
International
Language
English
International co-publication
Yes
Co-publication with a company
No
DOI
10.1007/s12220-022-01131-7
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes