Volume estimates and classification theorem for constant weighted mean\n curvature hypersurfaces

2019/12/06 by Saul Ancari, Ancari, Saul, Igor Miranda +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1912.03415

openalex publication_date 2019/12/06 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a classification for complete embedded constant\nweighted mean curvature hypersurfaces \Σ\⊂\ℝⁿ⁺¹. We\ncharacterize the hyperplanes and generalized round cylinders by using an\nintrinsic property on the norm of the second fundamental form. Furthermore, we\nprove an equivalence of properness, finite weighted volume and exponential\nvolume growth for submanifolds with weighted mean curvature of at most linear\ngrowth.\n

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