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Prescribed k-symmetric curvature hypersurfaces in de Sitter space

Part of: Global differential geometry Elliptic equations and systems

Published online by Cambridge University Press:  26 November 2020

Daniel Ballesteros-Chávez ,
Wilhelm Klingenberg  and
Ben Lambert
Daniel Ballesteros-Chávez
Affiliation:
Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100, Gliwice, Poland e-mail: danielyho@yahoo.com
Wilhelm Klingenberg
Affiliation:
Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom e-mail: wilhelm.klingenberg@durham.ac.uk
Ben Lambert*
Affiliation:
School of Electronics, Computing and Mathematics, University of Derby, Markeaton Street, Derby DE22 3AW, United Kingdom
*
e-mail: b.lambert@derby.ac.uk
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Abstract

We prove the existence of compact spacelike hypersurfaces with prescribed k-curvature in de Sitter space, where the prescription function depends on both space and the tilt function.

Keywords

Prescribed curvature equationsfully nonlinear elliptic equationssymmetric curvature functionsde Sitter spaceLorentz manifoldssemi-Riemannian manifoldsspacelike submanifoldstilt function

MSC classification

Primary: 35J60: Nonlinear elliptic equations
Secondary: 53C50: Lorentz manifolds, manifolds with indefinite metrics 53C42: Immersions (minimal, prescribed curvature, tight, etc.)

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 4 , December 2021 , pp. 886 - 901
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

D.B-C. was supported by CONACYT-Doctoral scholarship no. 411485. B.L. was supported by a Leverhulme Trust Research Project Grant RPG-2016-174.

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