Mediterranean Journal of Mathematics

, Volume 13, Issue 3, pp 1285–1290 | Cite as

Bernstein-type Theorems in a Riemannian Manifold with an Irrotational Killing Vector Field

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Abstract

The minimal hypersurface equation for a graph in a Riemannian manifold which admits a nowhere zero Killing vector field, whose orthogonal distribution is integrable, is studied. New uniqueness results for the entire solutions of this equation on a compact Riemannian manifold of arbitrary dimension are given. In particular, new Bernstein theorems are proved.

Keywords

Nonlinear PDE of divergence form uniqueness of entire solutions compact Riemannian manifolds killing vector fields 

Mathematics Subject Classification

58J05 35J93 53C42 53A10 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain
  2. 2.Departamento de Matemáticas, Campus de RabanalesUniversidad de CórdobaCórdobaSpain

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