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Removability of singular sets of harmonic maps. (English) Zbl 1026.58017
Summary: It is proved that a harmonic map with small energy and the monotonicity property is smooth if its singular set is rectifiable and has a finite uniform density; moreover, the monotonicity property holds if the singular set has a lower dimension or its gradient has higher integrability.
This work generalizes the results in D. Costa and G. Liao, J. Fac. Sci. Univ. Tokyo, 1A, 35, 321-344 (1988; Zbl 0662.58013), F. Duzaar and M. Fuchs, Ann. Inst. Henri Poincaré 7, 385-405 (1990; Zbl 0715.49040), G. Liao, J. Diff. Geom. 22, 233-241 (1985; Zbl 0619.58015) and Pac. J. Math. 131, 291-302 (1988; Zbl 0669.58010)], which were proved under the assumption that the singular sets are isolated points or smooth submanifolds.

MSC:
58E20 Harmonic maps, etc.
49Q20 Variational problems in a geometric measure-theoretic setting
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