An estimate for the Gauss curvature of minimal surfaces in \mathbb R^m whose Gauss map omits a set of hyperplanes

1996/04/23 by Robert Osserman, Min Ru, Osserman, Robert +1
Mathematics · #Analytic and geometric function theory #Combinatorics #Computer science #Curvature #Differential Geometry (math.DG) #FOS: Mathematics #Gauss #Gauss map #Gaussian curvature #Geometric Analysis and Curvature Flows #Geometry #Hyperplane #Mathematics #Mean curvature #Mean curvature flow #Physics #Point processes and geometric inequalities #Pure mathematics #Set (abstract data type) #Total curvature #math.DG

paper · pdf · doi:10.48550/arxiv.math/9604225

published in arXiv (Cornell University) (Cornell University)

arxiv created 1996/04/23 · openalex publication_date 1996/04/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We give an estimate of the Gauss curvature for minimal surfaces in \mathbb R^m whose Gauss map omits more than m(m+1)/2 hyperplanes in \mathbb P^m-1(\mathbb C).

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