Every closed embedded lambda-self-expander in Euclidean space is a round sphere centered at the origin, proved through a new weighted Heintze-Karcher inequality.
Alexandrov Theorem for constant weighted mean curvature surfaces
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abstract
We prove a Heintze--Karcher type inequality for a large class of log-convex weights in Euclidean and Hyperbolic spaces. As a consequence we obtain an Alexandrov theorem for $\lambda$-self expanders.
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An Alexandrov-type theorem in warped product manifolds with radial density
Every closed embedded lambda-self-expander in Euclidean space is a round sphere centered at the origin, proved through a new weighted Heintze-Karcher inequality.