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In this paper, we prove a classification for complete embedded constant weighted mean curvature hypersurfaces $Sigmasubsetmathbb{R}^{n+1}$. We characterize the hyperplanes and generalized round cylinders by using an intrinsic property on the norm of the second fundamental form. Furthermore, we prove an equivalence of properness, finite weighted volume and exponential volume growth for submanifolds with weighted mean curvature of at most linear growth.
In this article, we study hypersurfaces $Sigmasubset mathbb{R}^{n+1}$ with constant weighted mean curvature. Recently, Wei-Peng proved a rigidity theorem for CWMC hypersurfaces that generalizes Le-Sesum classification theorem for self-shrinker. More
In this paper, we study constant weighted mean curvature hypersurfaces in shrinking Ricci solitons. First, we show that a constant weighted mean curvature hypersurface with finite weighted volume cannot lie in a region determined by a special level s
Alexandrovs soap bubble theorem asserts that spheres are the only connected closed embedded hypersurfaces in the Euclidean space with constant mean curvature. The theorem can be extended to space forms and it holds for more general functions of the p
We obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete Riemannian manifold. Similar results are also given for complete spacelike hypersurfaces in Lorentzian ambient spaces.
In 1968, Simons introduced the concept of index for hypersurfaces immersed into the Euclidean sphere S^{n+1}. Intuitively, the index measures the number of independent directions in which a given hypersurface fails to minimize area. The earliest resu