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arXiv · 2007.04355

Rigidity for Bach-flat metrics on manifolds with boundary and applications

Matthew J. Gursky·Siyi Zhang
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Abstract

In the article we consider Bach-flat metrics on four-manifolds with boundary, with conformally invariant boundary conditions. We show that such metrics arise naturally as critical points of the Weyl energy under a constraint. We then prove a rigidity result: if a Yamabe metric associated to a critical metric when restricted to the boundary is isometric to the round three-sphere, then the critical metric must be isometric to the standard upper hemisphere.

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Matthew J. Gursky, Siyi Zhang. 2020-07-08. Rigidity for Bach-flat metrics on manifolds with boundary and applications. https://arxiv.org/abs/2007.04355

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