On stable hypersurfaces with constant mean curvature in Euclidean spacesReport as inadecuate



 On stable hypersurfaces with constant mean curvature in Euclidean spaces


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In this paper, we derive curvature estimates for strongly stable hypersurfaces with constant mean curvature immersed in $\mathbb{R}^{n+1}$, which show that the locally controlled volume growth yields a globally controlled volume growth if $\partial M=\emptyset$. Moreover, we deduce a Bernstein-type theorem for complete stable hypersurfaces with constant mean curvature of arbitrary dimension, given a finite $L^p$-norm curvature condition.



Author: Jinpeng Lu

Source: https://archive.org/







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