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Stability and singularities of harmonic maps into 3-spheres

✍ Scribed by Tôru Nakajima

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
145 KB
Volume
54
Category
Article
ISSN
0362-546X

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✦ Synopsis

The behavior of harmonic maps from a domain in R 4 into S 3 is discussed. In this paper, we show that if u is a strictly stable stationary harmonic map : B 4 → S 3 , such that the singular set Sing(u) of u consists of {0}, then the degree deg(u; 0) of u at 0 is zero; and that if u is a weakly stable harmonic map B 4 → S 3 with Sing(u) = {0}, then deg(u; 0) = 0 or ±1. Furthermore, the characterization of homogeneous stable stationary harmonic maps from B 4 into S 3 is given.

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