A new gap for $CMC$ biharmonic hypersurfaces in Euclidean spheres
Simona Nistor
TL;DR
This paper improves the known bounds on the mean curvature for complete constant mean curvature proper-biharmonic hypersurfaces in Euclidean spheres, refining the classification of such geometric objects.
Contribution
It provides an improved gap result that narrows the range of mean curvature values for these hypersurfaces, advancing the understanding of their geometric properties.
Findings
Refined the range of mean curvature for proper-biharmonic hypersurfaces
Enhanced classification criteria for CMC hypersurfaces in spheres
Contributed to the theory of biharmonic submanifolds
Abstract
In this note we improve a gap result concerning the range of the mean curvature of complete proper-biharmonic hypersurfaces in unit Euclidean spheres.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Holomorphic and Operator Theory