Regular article

Computing and Visualization in Science

, Volume 7, Issue 1, pp 53-59

First online:

Construction of harmonic map flows through the method of discrete Morse flows

  • Jun-ichi HagaAffiliated withDepartment of Mathematics, Keio University
  • , Keisuke HoshinoAffiliated withDepartment of Mathematics, Chiba Institute of Technology
  • , Norio KikuchiAffiliated withDepartment of Mathematics, Keio University Email author 

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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 [11], where a target manifold has the bounded positive curvature.