Translators of the Mean Curvature Flow in Hyperbolic Einstein’s Static Universe

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Ortega M., Yalçın B.

International Electronic Journal of Geometry, cilt.17, sa.1, ss.157-170, 2024 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.36890/iejg.1437356
  • Dergi Adı: International Electronic Journal of Geometry
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.157-170
  • Anahtar Kelimeler: elliptic PDEs, horospheres, hyperbolic Einstein’s static universe, hyperbolic space, mean curvature flow, rotationally invariant, Translator
  • Ankara Üniversitesi Adresli: Evet

Özet

In this study, we deal with non-degenerate translators of the mean curvature flow in the wellknown hyperbolic Einstein’s static universe. We classify translators foliated by horospheres and rotationally invariant ones, both space-like and time-like. For space-like translators, we show a uniqueness theorem as well as a result to extend an isometry of the boundary of the domain to the whole translator, under simple conditions. As an application, we obtain a characterization of the the bowl when the boundary is a ball, and of certain translators foliated by horospheres whose boundary is a rectangle.