Mapping problems, fundamental groups and defect measures |
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Authors: | Fanghua Lin |
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Institution: | (1) Courant Institute of Mathematics, New York University, 10012 New York, NY, USA |
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Abstract: | We study all the possible weak limits of a minimizing sequence, for p-energy functionals, consisting of continuous maps between Riemannian manifolds subject to a Dirichlet boundary condition
or a homotopy condition. We show that if p is not an integer, then any such weak limit is a strong limit and, in particular, a stationary p-harmonic map which is C
1,α continuous away from a closed subset of the Hausdorff dimension ≤ n − p] − 1. If p is an integer, then any such weak limit is a weakly p-harmonic map along with a (n − p)-rectifiable Radon measure μ. Moreover, the limiting map is C
1,α continuous away from a closed subset Σ=spt μ ∪ S with H
n − p
(S)=0. Finally, we discuss the possible varifolds type theory for Sobolev mappings.
Partially supported by NSF Grant DMS 9626166 |
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Keywords: | Defect measure Harmonic mapping Generalized varifold Rectifiability |
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