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

Abstract

By using Gromov's $\mu$-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.

arXiv comment20 pages, 1 figure, All comments are welcome

References in corpus (5)

• Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds
• Deformations of the hemisphere that increase scalar curvature
• Scalar curvature estimates for compact symmetric spaces
• Nonnegative Scalar Curvature and Area Decreasing Maps
• Nonnegative scalar curvature and area decreasing maps on complete foliated manifolds

Cited by in corpus (3)

• Scalar curvature rigidity of warped product metrics
• Rigidity and Non-Rigidity of ${\mathbb{H}}^n/{\mathbb{Z}}^{n-2}$ with Scalar Curvature Bounded from Below
• The degree condition in Llarull's theorem on scalar curvature rigidity