Stable stationary harmonic maps to spheres

Fang Hua Lin; Chang You Wang

doi:10.1007/s10114-005-0673-7

Stable stationary harmonic maps to spheres

Fang Hua Lin, Chang You Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	319-330
Number of pages	12
Journal	Acta Mathematica Sinica, English Series
Volume	22
Issue number	2
DOIs	https://doi.org/10.1007/s10114-005-0673-7
State	Published - Apr 2006

Keywords

Hausdorff dimension
Rectifiablity
Stable stationary harmonic map

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s10114-005-0673-7

Cite this

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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 H{\"o}lder continuous curves. We also discuss the minimization problem among continuous maps from B n to S 2.",

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AU - Lin, Fang Hua

AU - Wang, Chang You

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AB - 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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KW - Rectifiablity

KW - Stable stationary harmonic map

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Stable stationary harmonic maps to spheres

Abstract

Keywords

ASJC Scopus subject areas

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