Construction of harmonic map flows through the method of discrete Morse flows
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By the method of discrete Morse flows, we construct the Morse flow of harmonic map from a Riemannian manifold with measurable and bounded metric into that with Alexander non-positive curvature. The construction is directly derived without isometrically embedding of the target manifold into Euclidean space. Our method will be in force in the case, as treated in , where a target manifold has the bounded positive curvature.
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