@article{Wang2026, 
author = {Jiahui Wang and Liu Yang},
title = {Strongly stable hypersurfaces with constant mean curvature in space forms},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {10},
pages = {7261-7273},
keywords = {constant mean curvature, finite Lp norm curvature, stability},
url = {https://www.sciopen.com/article/10.3934/era.2026314},
doi = {10.3934/era.2026314},
abstract = {In this paper, we consider a complete strongly stable hypersurface        M    n   with constant mean curvature (CMC)    H in        N          n      +      1        (  κ  ), where    2  ≤  n  ≤  5, and prove that        M    n   is totally umbilical if        H    2    +  κ  >  0 and the        L    2   norm curvature satisfies some growth conditions. In addition, we obtain that a complete stable hypersurface        M    n   in        N          n      +      1        (  κ  )  (  n  =  3  ,  4  ,  5  ) with CMC is a geodesic sphere if    −      H    2    <  κ  ≤  0 and        M    n   has some finite        L    p   norm curvature.}
}