Geometric barriers for the existence of hypersurfaces with prescribed curvatures in Mⁿ× R

2014/05/29 by José A. Gálvez, Gálvez, José A., Victorino Lozano +1
Mathematics · #53A10 #58J05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.DG #msc:53A10 #msc:58J05

paper · pdf · doi:10.48550/arxiv.1405.7502

arxiv created 2014/05/29 · openalex publication_date 2014/05/29 · arxiv updated 2014/05/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We show the existence of a deformation process of hypersurfaces from a product space M₁× R into another product space M₂× R such that the relation of the principal curvatures of the deformed hypersurfaces can be controlled in terms of the sectional curvatures or Ricci curvatures of M₁ and M₂. In this way, we obtain barriers which are used for proving existence or non existence of hypersurfaces with prescribed curvatures in a general product space M× R.

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