MINIMIZING 1/2-HARMONIC MAPS INTO SPHERES

Abstract : In this article, we improve the partial regularity theory for minimizing 1/2-harmonic maps of [30, 33] in the case where the target manifold is the (m − 1)-dimensional sphere. For m>2, we show that minimizing 1/2-harmonic maps are smooth in dimension 2, and have a singular set of codimension at least 3 in higher dimensions. For m=2, we prove that, up to an orthogonal transformation , x/|x| is the unique non trivial 0-homogeneous minimizing 1/2-harmonic map from the plane into the circle S1. As a corollary, each point singularity of a minimizing 1/2-harmonic maps from a 2d domain into S1 has a topological charge equal to ±1.
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https://hal.archives-ouvertes.fr/hal-01985037
Contributor : Vincent Millot <>
Submitted on : Thursday, January 17, 2019 - 3:20:37 PM
Last modification on : Wednesday, May 15, 2019 - 3:41:57 AM

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  • HAL Id : hal-01985037, version 1

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Vincent Millot, Marc Pegon. MINIMIZING 1/2-HARMONIC MAPS INTO SPHERES. 2019. ⟨hal-01985037⟩

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