Rotationally invariant translators of the mean curvature flow in Einstein's static universe

Ortega M., YILDIRIM H.

Differential Geometry and its Application, cilt.95, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 95
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.difgeo.2024.102153
  • Dergi Adı: Differential Geometry and its Application
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: Einstein's static universe, Elliptic PDEs, Mean curvature flow, Rotationally invariant, Translator
  • İstanbul Üniversitesi Adresli: Evet

Özet

In this paper, we deal with non-degenerate translators of the mean curvature flow in the well-known Einstein's static universe. We focus on the rotationally invariant translators, that is, those invariant by a natural isometric action of the special orthogonal group on the ambient space. In the classification list, there are three space-like cases and five time-like cases. All of them, except a totally geodesic example, have one or two conic singularities. Also, we show a uniqueness result based on the behaviour of the translator on its boundary. As an application, we extend an isometry of the sphere to the whole translator under simple conditions. This leads to a characterization of a bowl-like example.