Stable Stationary Harmonic Maps to Spheres

Stable Stationary Harmonic Maps to Spheres

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摘要 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 B5 to 83 is the union of finitely many isolated singular points and finitely many HSlder continuous curves. We also discuss the minimization problem among continuous maps from B^n to S^2. 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 B5 to 83 is the union of finitely many isolated singular points and finitely many HSlder continuous curves. We also discuss the minimization problem among continuous maps from B^n to S^2.

作者 Fang Hua LIN Chang You WANG

机构地区 Courant Institute of Mathematical Sciences Department of Mathematics

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第2期319-330,共12页 数学学报（英文版）

基金 partially supported by NSF

关键词 stable stationary harmonic map Hausdorff dimension rectifiablity stable stationary harmonic map, Hausdorff dimension, rectifiablity

分类号 O174 [理学—基础数学]

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Acta Mathematica Sinica,English Series

2006年第2期

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Stable Stationary Harmonic Maps to Spheres

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