Moving monotonicity formulae for minimal submanifolds in constant curvature

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE 2026 Open access

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Authors: Jonathan J. Zhu, Keaton Naff
DOI: 10.2422/2036-2145.202411_001
Cited by: 0

Abstract

We discover new monotonicity formulae for minimal submanifolds in space forms, which imply the sharp area bound for minimal submanifolds through a prescribed point in a geodesic ball. These monotonicity formulae involve an energy-like integral over sets which are, in general, not geodesic balls. In the Euclidean case, these sets reduce to the moving-centre balls introduced by the second author in [Zhu18].

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Advanced Differential Geometry Research Nonlinear Partial Differential Equations

Publication details

Journal / source
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
Pages
12–12
Publication date
22 January 2026
Language
IT