The rectified n-harmonic map flow with applications to homotopy classes

• Min-Chun Hong ^[1]
  1. [1] University of Queensland

     University of Queensland

     Australia

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 18, Nº 4, 2018, págs. 1249-1283
• Idioma: inglés
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• Resumen

  • We introduce a rectified n-harmonic map flow from an n-dimensional closed Riemannian manifold to another closed Riemannian manifold. We prove existence of a global solution, which is regular except for a finite number of points, of the rectified n-harmonic map flow and establish an energy identity for the flow at each singular time. Finally, we present two applications of the rectified n-harmonic map flow to minimizing the n-energy functional and the Dirichlet energy functional in a homotopy class.