Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 014, 13 pages      arXiv:2306.17760      https://doi.org/10.3842/SIGMA.2024.014
Contribution to the Special Issue on Differential Geometry Inspired by Mathematical Physics in honor of Jean-Pierre Bourguignon for his 75th birthday

A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary

Alessandro Carlotto a and Chao Li b
a) Università di Trento, Dipartimento di Matematica, via Sommarive 14, 38123 Trento, Italy
b) New York University - Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA

Received July 03, 2023, in final form January 31, 2024; Published online February 13, 2024

Abstract
We study notions of isotopy and concordance for Riemannian metrics on manifolds with boundary and, in particular, we introduce two variants of the concept of minimal concordance, the weaker one naturally arising when considering certain spaces of metrics defined by a suitable spectral ''stability'' condition. We develop some basic tools and obtain a rather complete picture in the case of surfaces.

Key words: positive scalar curvature; isotopy; concordance; free boundary minimal surfaces.

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