Closed embedded constant weighted mean curvature hypersurfaces in the expander space are centered spheres, proved through a weighted Heintze-Karcher inequality.
An Alexandrov-type theorem in warped product manifolds with radial density
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper, we establish a Heintze--Karcher inequality for closed embedded hypersurfaces in a class of warped product manifolds endowed with radial density. As a consequence, we prove Alexandrov-type theorem for constant weighted mean curvature hypersurfaces in such spaces. In particular, we prove that a closed embedded $\lambda$-self-expander in the Euclidean space must be a round sphere centered at the origin.
citation-role summary
background 1
citation-polarity summary
fields
math.DG 1years
2026 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Alexandrov Theorem for constant weighted mean curvature surfaces
Closed embedded constant weighted mean curvature hypersurfaces in the expander space are centered spheres, proved through a weighted Heintze-Karcher inequality.