Soliton solutions to the curve shortening flow on the 2-dimensional hyperbolic space

• Fábio Nunes da Silva ^[1] ; Keti Tenenblat ^[1]
  1. [1] Universidade de Brasília

     Universidade de Brasília

     Brasil

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 6, 2022, págs. 1763-1782
• Idioma: inglés
• DOI: 10.4171/RMI/1343
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• Resumen

  • We show that a curve is a soliton solution to the curve shortening flow on the 2-dimensional hyperbolic space if and only if its geodesic curvature can be written as the inner product between its tangent vector field and a fixed vector of the 3-dimensionalMinkowski space.We show that for each fixed vector there is a 2-parameter family of soliton solutions to the flow. We prove that there are three classes of such curves. Moreover, we prove that each soliton is defined on the whole real line, it is embedded and its geodesic curvature, at each end, converges to a constant