Article ID Journal Published Year Pages File Type
5775022 Journal of Mathematical Analysis and Applications 2017 20 Pages PDF
Abstract
A. Arvanitoyeorgos and G. Kaimakamis proposed in [1] the conjecture that: any hypersurface satisfying ΔH→=λH→ in pseudo-Euclidean space Esn+1 of index s has constant mean curvature. In this paper, we prove that the conjecture is true when the hypersurfaces have at most two distinct principal curvatures. Then, we estimate that constant mean curvature, and give its explicit expression for some special cases. As a result, for that of Lorentzian type hypersurfaces which are not minimal, we prove that it must be isoparametric and give classification results.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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