On uniqueness of heat flow of harmonic maps
نویسندگان
چکیده
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 Sk−1 or a Riemannian homogeneous manifold. For such a class of solutions, we also establish the convexity property of the Dirichlet energy for t ≥ t0 > 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 whose gradients belong to LqtL l x, for q > 2 and l > n satisfying the Serrin’s condition.
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