Unique Continuation Property for Biharmonic Hypersurfaces in Spheres

2020/07/13 by Bibi, Hiba, Loubeau, Eric, Oniciuc, Cezar · 1 citation
#31B30 #53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.06527

Abstract

We study properties of non-minimal biharmonic hypersurfaces of spheres. The main result is a CMC Unique Continuation Theorem for biharmonic hypersurfaces of spheres. We then deduce new rigidity theorems to support the Conjecture that biharmonic submanifolds of Euclidean spheres must be of constant mean curvature.

Cited by

• Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature

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