Beijing Journal of Pure and Applied Mathematics

Volume 1 (2024)

Number 2

Attaching faces of positive scalar curvature manifolds with corners

Pages: 659 – 688

DOI: https://dx.doi.org/10.4310/BPAM.2024.v1.n2.a6

Authors

Alessandro Carlotto (Dipartimento di Matematica, Università di Trento, Trento, Italy)

Chao Li (Courant Institute, New York University, New York. NY, USA)

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.

Keywords

scalar curvature, mean curvature, desingularization constructions, free boundary minimal hypersurfaces

2010 Mathematics Subject Classification

Primary 53C21. Secondary 53A10, 58J90.

Full Text (PDF format)

In memory of Robert Bartnik

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 947923). C.L. was supported by an NSF grant (DMS- 2202343) and a Simons Junior Faculty Fellowship.

Received 10 August 2023

Accepted 9 January 2024

Published 17 July 2024