Nonexistence of DEC spin fill-ins

TL;DR

This paper proves that certain closed spin manifolds cannot be filled with a spin manifold satisfying the dominant energy condition if a specific curvature function exceeds a threshold.

Contribution

It establishes a nonexistence result for DEC fill-ins of closed spin manifolds under curvature constraints, advancing understanding of geometric and physical conditions.

Findings

No DEC fill-in exists when the generalized mean curvature is sufficiently large.

The result links curvature bounds to fill-in obstructions.

Provides a new criterion for the nonexistence of certain geometric fillings.

Abstract

In this note, we show that a closed spin Riemannian manifold does not admit a spin fill-in satisfying the dominant energy condition (DEC) if a certain generalized mean curvature function is point-wise large.