Horizons in noncompact fill-ins of nonnegative scalar curvature

TL;DR

This paper investigates conditions under which a complete nonnegative scalar curvature metric on a 3-manifold with boundary admits a closed minimal surface, advancing understanding of geometric structures in noncompact fill-ins.

Contribution

It establishes new conditions that guarantee the existence of a closed minimal surface in noncompact fill-ins with nonnegative scalar curvature.

Findings

Existence of closed minimal surfaces under specific geometric conditions

Conditions linking scalar curvature and minimal surface existence

Advancement in understanding fill-ins of nonnegative scalar curvature

Abstract

Given a complete Riemannian metric of nonnegative scalar curvature on $\Sigma \times (-\infty, 0 ] $, where $\Sigma$ denotes a $2$-sphere, we exhibit conditions that imply the existence of a closed minimal surface homologous to the boundary.