Attaching faces of positive scalar curvature manifolds with corners

TL;DR

This paper introduces a new desingularization technique for smoothly attaching manifolds with corners, ensuring control over scalar and mean curvatures, advancing geometric analysis methods.

Contribution

It presents a novel theorem for gluing manifolds with corners while controlling scalar and mean curvatures, enhancing tools for geometric topology.

Findings

Successful construction of smooth attachments with curvature control

Extension of desingularization techniques to manifolds with corners

Potential applications in geometric topology and scalar curvature studies

Abstract

We prove a novel desingularization theorem, that allows to smoothly attach two given manifolds with corners by suitably gluing a pair of isometric faces, with control on both the scalar curvature of the resulting space and the mean curvature of its boundary.