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

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.

invited contribution to a special issue of SIGMA, in honor of Jean-Pierre Bourguignon on the occasion of his 75th birthday

References in corpus (4)

• Boundary conditions for scalar curvature
• Riemannian Penrose inequality via Nonlinear Potential Theory
• Metrics with ${\lambda }_1(-\Delta +kR)\ge 0$ and flexibility in the Riemannian Penrose Inequality
• Positive scalar curvature on manifolds with boundary and their doubles