Positive scalar curvature on manifolds with boundary and their doubles

Abstract

This paper is about positive scalar curvature on a compact manifold $X$ with non-empty boundary $\partial X$. In some cases, we completely answer the question of when $X$ has a positive scalar curvature metric which is a product metric near $\partial X$, or when $X$ has a positive scalar curvature metric with positive mean curvature on the boundary, and more generally, we study the relationship between boundary conditions on $\partial X$ for positive scalar curvature metrics on $X$ and the positive scalar curvature problem for the double $M=\mathrm{Dbl}(X,\partial X)$.

26 pages, 9 figures. A number of small errors corrected and two new references added

References in corpus (1)

• Boundary conditions for scalar curvature

Cited by in corpus (2)

• Relative eta invariant and uniformly positive scalar curvature on non-compact manifolds
• A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary