AI 中文总结
本文针对带径向密度的扭曲积流形，建立Heintze--Karcher不等式，进而证明常加权平均曲率超曲面的亚历山德罗夫型定理，还得出欧氏空间中闭嵌入λ-自展子必为中心在原点的圆球的结论。
AI 中文摘要
本文针对一类带有径向密度的扭曲积流形中的闭嵌入超曲面，建立了Heintze--Karcher不等式。作为推论，证明了这类空间中常加权平均曲率超曲面的亚历山德罗夫型定理。特别地，证明了欧氏空间中的闭嵌入λ-自展子必为以原点为中心的圆球。
英文摘要
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 $λ$-self-expander in the Euclidean space must be a round sphere centered at the origin.
Comments21 pages
