Mean Curvature in Minkowski Spaces

  1. Cabezas Rivas, Esther 1
  2. Miquel, Vicente 1
  1. 1 Universitat de València
    info

    Universitat de València

    Valencia, España

    ROR https://ror.org/043nxc105

Libro:
Proceedings of the Conference Contemporary Geometry and related topics

Editorial: Faculty of Mathematics, University of Belgrade

ISBN: 86-7589-059-1

Año de publicación: 2006

Páginas: 81-97

Tipo: Capítulo de Libro

GOOGLE SCHOLAR

Resumen

Considering the finite dimensional normed spaces with smooth and strictly convex unit sphere, the authors face to different notions of mean curvature. They explore the various natural definitions of volume and define the mean curvature as the first variation of the area. After recalling the basic notions of Minkowski spaces, volume and mean curvature associated to a definition of volume, they focus on showing the advantages and disadvantages of the definitions of mean curvature arising from the Hausdorff and Holmes–Thompson notions of volume and they discuss if they are in agreement with the concept of mean curvature arising in a variational problem on the volume of a hypersurface.