Hypersurfaces with H_r+1=0 in H x R

2015/03/25 by Maria Fernanda Elbert, Elbert, Maria Fernanda, Barbara Nelli +3
Mathematics · #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.DG #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1503.07489

openalex publication_date 2015/03/25 · arxiv created 2015/08/11 · arxiv updated 2015/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of rotational hypersurfaces in ℍⁿ× ℝ with H_r+1=0 and we classify them. Then we prove some uniqueness theorems for r-minimal hypersurfaces with a given (finite or asymptotic) boundary. In particular, we obtain a Schoen-type Theorem for two ended complete hypersurfaces.

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