Details
| Original language | English |
|---|---|
| Article number | 11 |
| Journal | Annals of Global Analysis and Geometry |
| Volume | 64 |
| Issue number | 2 |
| Early online date | 2 Aug 2023 |
| Publication status | Published - 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.
Keywords
- Generalized Robertson–Walker space-times, Mean curvature flow, Non-compactness, Prescribed mean curvature
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Geometry and Topology
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In: Annals of Global Analysis and Geometry, Vol. 64, No. 2, 11, 09.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Prescribed mean curvature flow of non-compact space-like Cauchy hypersurfaces
AU - Gentile, Giuseppe
AU - Vertman, Boris
N1 - Funding Information: The authors wish to thank the University of Oldenburg for the financial support and hospitality.
PY - 2023/9
Y1 - 2023/9
N2 - 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.
AB - 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.
KW - Generalized Robertson–Walker space-times
KW - Mean curvature flow
KW - Non-compactness
KW - Prescribed mean curvature
UR - http://www.scopus.com/inward/record.url?scp=85167439442&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2202.02424
DO - 10.48550/arXiv.2202.02424
M3 - Article
AN - SCOPUS:85167439442
VL - 64
JO - Annals of Global Analysis and Geometry
JF - Annals of Global Analysis and Geometry
SN - 0232-704X
IS - 2
M1 - 11
ER -