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Rigidity of 3D spherical caps via $\mu$-bubbles

Yuhao Hu, Peng Liu and Yuguang Shi

Vol. 323 (2023), No. 1, 89–114
DOI: 10.2140/pjm.2023.323.89
Abstract

By using Gromov’s μ-bubble technique, we show that the 3-dimensional spherical caps are rigid under perturbations that do not reduce the metric, the scalar curvature, and the mean curvature along its boundary. Several generalizations of this result will be discussed.

Keywords
Llarull's theorem, spherical cap, $ \mu$-bubble
Mathematical Subject Classification
Primary: 53C21
Secondary: 53C24
Milestones
Received: 27 May 2022
Revised: 23 January 2023
Accepted: 25 March 2023
Published: 29 May 2023
Authors
Yuhao Hu
Key Laboratory of Pure and Applied Mathematics
Peking University
Beijing
China
Peng Liu
Key Laboratory of Pure and Applied Mathematics
Peking University
Beijing
China
Yuguang Shi
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences
Peking University
Beijing
China

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