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• W1491238316 abstract "In this paper, we establish the uniqueness of heat flow of harmonic maps into (N, h) that have sufficiently small renormalized energies, provided that N is either a unit sphere $S^{k-1}$ or a compact Riemannian homogeneous manifold without boundary. For such a class of solutions, we also establish the convexity property of the Dirichlet energy for $tge t_0>0$ and the unique limit property at time infinity. As a corollary, the uniqueness is shown for heat flow of harmonic maps into any compact Riemannian manifold N without boundary whose gradients belong to $L^q_t L^l_x$ for $q>2$ and $l>n$ satisfying the Serrin's condition." @default.
• W1491238316 created "2016-06-24" @default.
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• W1491238316 date "2012-08-07" @default.
• W1491238316 modified "2023-09-23" @default.
• W1491238316 title "On uniqueness of heat flow of harmonic maps" @default.
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• W1491238316 doi "https://doi.org/10.48550/arxiv.1208.1470" @default.
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