Removability of singular sets of harmonic maps | Zendy

Libin Mou | Zendy

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Removability of singular sets of harmonic maps

Author(s) -

Libin Mou

Publication year - 1994

Publication title -

archive for rational mechanics and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.933

H-Index - 106

eISSN - 1432-0673

pISSN - 0003-9527

DOI - 10.1007/bf00381158

Subject(s) - monotonic function , mathematics , harmonic map , dimension (graph theory) , property (philosophy) , harmonic , singular point of a curve , mathematical analysis , pure mathematics , work (physics) , set (abstract data type) , singular solution , physics , computer science , philosophy , epistemology , quantum mechanics , thermodynamics , programming language

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 [CL, DF, LG12], which were proved under the assumption that the singular sets are isolated points or smooth submanifolds.

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