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A prescribed scalar and boundary mean curvature problem on compact manifolds with boundary

We consider the problem of finding a metric in a given conformal class with prescribed nonpositive scalar curvature and nonpositive boundary mean curvature on a compact manifold with boundary, and establish a necessary and sufficient condition in terms of a conformal invariant that measures the zero set of the target curvatures.

preprint2021arXivOpen access
Vladmir SiccaGantumur Tsogtgerel
math.APmath.DG
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Vladmir SiccaGantumur Tsogtgerel

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