Convergence of Minimal Submanifolds to a Singular Variety

  • Robert Gulliver
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)

Abstract

A sequence of minimal hypersurfaces M h is considered, whose varifold limit V is not a density-one smooth hypersurface. Six geometrical problems are outlined, with the idea of studying asymptotic behavior as h → ∞ in terms of additional structures on V. Variational limits for the Dirichlet integral are presented in some detail; the examples involve homogenization of manifolds.

Keywords

Riemannian Manifold Minimal Surface Minimal Hypersurface Nonnegative Borel Measure DIRICHLET Integral 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Robert Gulliver
    • 1
  1. 1.Department of MathematicsUniversity of MinnesotaMinneapolisUSA

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