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A note on scalar curvature and the convexity of boundaries

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.

preprint2012arXivOpen access
Martin Reiris
math.DG
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Martin Reiris

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