Stable Stationary Harmonic Maps to Spheres |
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| Authors: | Fang Hua Lin Chang You Wang |
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| Institution: | (1) Courant Institute of Mathematical Sciences, New York University, NY 10012, USA;(2) Department of Mathematics, University of Kentucky, Lexington, KY 40513, USA |
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| Abstract: | For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable–stationary harmonic maps to the sphere S k . We show that the singular set of stable–stationary harmonic maps from B 5 to S 3 is the union of finitely many isolated singular points and finitely many Hölder continuous curves. We also discuss the minimization problem among continuous maps from B n to S 2. |
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| Keywords: | stable stationary harmonic map Hausdorff dimension rectifiablity |
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