Convergence of Minimal Submanifolds to a Singular Variety
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.
KeywordsRiemannian Manifold Minimal Surface Minimal Hypersurface Nonnegative Borel Measure DIRICHLET Integral
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