@article{Yang2022, 
author = {Dan Yang and Jinchao Yu and Jingjing Zhang and Xiaoying Zhu},
title = {A class of hypersurfaces in              E              s              n      +      1       satisfying    Δ            H      →        =  λ            H      →},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {39-53},
keywords = {proper mean curvature vector, linear Weingarten hypersurfaces, principal curvatures},
url = {https://www.sciopen.com/article/10.3934/math.2022003},
doi = {10.3934/math.2022003},
abstract = {A nondegenerate hypersurface in a pseudo-Euclidean space              E              s              n      +      1       is called to have proper mean curvature vector if its mean curvature              H      →       satisfies    Δ            H      →        =  λ            H      →       for a constant    λ. In 2013, Arvanitoyeorgos and Kaimakamis conjectured [1]: any hypersurface satisfying    Δ            H      →        =  λ            H      →       in pseudo-Euclidean space              E              s              n      +      1       has constant mean curvature. This paper will give further support evidences to this conjecture by proving that a linear Weingarten hypersurface        M          r              n       in              E              s              n      +      1       satisfying    Δ            H      →        =  λ            H      →       has constant mean curvature if        M          r              n       has diagonalizable shape operator with less than seven distinct principal curvatures.}
}