Unique Continuation Property for Biharmonic Hypersurfaces in Spheres
Hiba Bibi, Eric Loubeau, and Cezar Oniciuc
TL;DR
This paper proves a unique continuation property for biharmonic hypersurfaces in spheres and derives rigidity results supporting the conjecture that such submanifolds have constant mean curvature.
Contribution
It establishes a CMC unique continuation theorem for biharmonic hypersurfaces in spheres and provides new rigidity theorems related to the conjecture.
Findings
Proved a CMC unique continuation theorem for biharmonic hypersurfaces in spheres
Derived new rigidity theorems supporting the conjecture on biharmonic submanifolds
Contributed to understanding the structure of biharmonic hypersurfaces in spherical geometry
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.