Llarull's theorem on noncompact manifolds with boundary

TL;DR

This paper extends Llarull's theorem to noncompact manifolds with compact boundary, broadening its applicability in geometric analysis and spin geometry.

Contribution

It generalizes previous results to include noncompact manifolds with boundary, filling a gap in the existing geometric and spin manifold theory.

Findings

Extended Llarull's theorem to noncompact manifolds with boundary

Provided new geometric inequalities for spin manifolds

Enhanced understanding of boundary effects in noncompact geometric settings

Abstract

Recently, Zhang \cite{Zh20} and Li-Su-Wang-Zhang \cite{LSWZ24+} generalized Llarull's theorem to the noncompact complete spin manifold. In this paper, we further extend their results to the noncompact manifold with compact boundary.