A note on scalar curvature and the convexity of boundaries
Differential Geometry
2012-09-21 v1
Abstract
We prove that any smooth Riemannian manifold of non-negative scalar curvature and with a strictly mean convex and compact boundary component can be (C^2) extended beyond the component to have non-negative scalar curvature and to enjoy anyone of the following three types of (new) boundary: strictly convex, totally geodesic or strictly concave. The extension procedure can be applied for instance to "positive mass" type of theorems.
Keywords
Cite
@article{arxiv.1209.4525,
title = {A note on scalar curvature and the convexity of boundaries},
author = {Martin Reiris},
journal= {arXiv preprint arXiv:1209.4525},
year = {2012}
}