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Rigidity for Bach-flat metrics on manifolds with boundary and applications by Gursky, Matthew J.; Zhang, Siyi is a scholarly article available to read on EtoBox.

What is Rigidity for Bach-flat metrics on manifolds with boundary and applications about?

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.

Author

Gursky, Matthew J.; Zhang, Siyi

Published

2020

Language

EN