Mean curvature and compactification of surfaces in a negatively curved Cartan-Hadamard manifold

2012/06/28 by A. Esteve, Antonio Esteve, Vicente Palmer +2
Mathematics · #53C20 #53C40 (Primary) 53C42 #57N05 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C20 #msc:53C40 #msc:53C42 #msc:57N05

paper · pdf · doi:10.48550/arxiv.1206.6748

24 pages

arxiv created 2012/06/28 · openalex publication_date 2012/06/28 · arxiv updated 2012/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We state and prove a Chern-Osserman-type inequality in terms of the volume growth for complete surfaces with controlled mean curvature properly immersed in a Cartan-Hadamard manifold N with sectional curvatures bounded from above by a negative quantity K_N≤ b<0

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