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arXiv · 2008.11893

Deformation of the scalar curvature and the mean curvature

Pak Tung Ho·Yen-Chang Huang
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Abstract

On a compact manifold $M$ with boundary $\partial M$, we study the problem of prescribing the scalar curvature in $M$ and the mean curvature on the boundary $\partial M$ simultaneously. To do this, we introduce the notion of singular metric, which is inspired by the early work of Fischer-Marsden in [18] and Lin-Yuan in [23] for closed manifold. We show that we can prescribe the scalar curvature and the mean curvature simultaneously for generic scalar-flat manifolds with minimal boundary. We also prove some rigidity results for the flat manifolds with totally geodesic boundary.

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Pak Tung Ho, Yen-Chang Huang. 2020-08-27. Deformation of the scalar curvature and the mean curvature. https://arxiv.org/abs/2008.11893

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