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Partial regularity for weak heat flows into spheres
Author(s) -
Chen Yunmei,
Li Jiayu,
Lin FangHua
Publication year - 1995
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160480403
Subject(s) - mathematics , hausdorff space , hausdorff measure , riemannian manifold , spheres , harmonic map , boundary (topology) , monotonic function , mathematical analysis , flow (mathematics) , heat flow , zero (linguistics) , pure mathematics , hausdorff dimension , geometry , thermal , physics , astronomy , linguistics , philosophy , meteorology
In this paper we show that a weak heat flow of harmonic maps from a compact Riemannian manifold (possibly with boundary) into a sphere, satisfying the monotonicity inequality and the energy inequality, is regular off a closed set of m ‐dimensional Hausdorff measure zero.