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Author Millot, Vincent ♦ Pegon, Marc
Source Hyper Articles en Ligne (HAL)
Content type Text
File Format PDF
Language English
Subject Keyword math ♦ Mathematics [math]/Analysis of PDEs [math.AP]
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.
Educational Use Research
Learning Resource Type Article