Nonexistence of NNSC fill-ins with large mean curvature

Abstract

In this note we show that a closed Riemannian manifold does not admit a fill-in with nonnegative scalar curvature if the mean curvature is point-wise large. Similar result also holds for fill-ins with a negative scalar curvature lower bound.

arXiv comment5 pages

References in corpus (4)

• Isometric embeddings into the Minkowski space and new quasi-local mass
• Scalar curvature and singular metrics
• Scalar Curvature of Manifolds with Boundaries: Natural Questions and Artificial Constructions
• On the Fill-in of Nonnegative Scalar Curvature Metrics

Cited by in corpus (1)

• Nonexistence of NNSC-cobordism of Bartnik data