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)


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.


Riemannian Manifold Minimal Surface Minimal Hypersurface Nonnegative Borel Measure DIRICHLET Integral 
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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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