Prescribed mean curvature flow of non-compact space-like Cauchy hypersurfaces

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Giuseppe Gentile
  • Boris Vertman

Organisationseinheiten

Externe Organisationen

  • Carl von Ossietzky Universität Oldenburg
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer11
FachzeitschriftAnnals of Global Analysis and Geometry
Jahrgang64
Ausgabenummer2
Frühes Online-Datum2 Aug. 2023
PublikationsstatusVeröffentlicht - Sept. 2023

Abstract

In this paper we consider the prescribed mean curvature flow of a non-compact space-like Cauchy hypersurface of bounded geometry in a generalized Robertson–Walker space-time. We prove that the flow preserves the space-likeness condition and exists for infinite time. We also prove convergence in the setting of manifolds with boundary. Our discussion generalizes previous work by Ecker, Huisken, Gerhardt and others with respect to a crucial aspects: we consider any non-compact Cauchy hypersurface under the assumption of bounded geometry. Moreover, we specialize the aforementioned works by considering globally hyperbolic Lorentzian space-times equipped with a specific class of warped product metrics.

ASJC Scopus Sachgebiete

Zitieren

Prescribed mean curvature flow of non-compact space-like Cauchy hypersurfaces. / Gentile, Giuseppe; Vertman, Boris.
in: Annals of Global Analysis and Geometry, Jahrgang 64, Nr. 2, 11, 09.2023.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Gentile G, Vertman B. Prescribed mean curvature flow of non-compact space-like Cauchy hypersurfaces. Annals of Global Analysis and Geometry. 2023 Sep;64(2):11. Epub 2023 Aug 2. doi: 10.48550/arXiv.2202.02424, 10.1007/s10455-023-09914-z
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