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ON THE EXISTENCE OF $f$-MAXIMAL SPACELIKE HYPERSURFACES IN CERTAIN WEIGHTED MANIFOLDS

Part of: Classical differential geometry Global differential geometry Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  02 May 2017

ARLANDSON M. S. OLIVEIRA Open the ORCID record for ARLANDSON M. S. OLIVEIRA [Opens in a new window]  and
HENRIQUE F. DE LIMA Open the ORCID record for HENRIQUE F. DE LIMA [Opens in a new window]
ARLANDSON M. S. OLIVEIRA
Affiliation:
Departamento de Matemática, Universidade Federal de Campina Grande, 58429-970 Campina Grande, Paraíba, Brazil email arlandsonm@gmail.com
HENRIQUE F. DE LIMA*
Affiliation:
Departamento de Matemática, Universidade Federal de Campina Grande, 58429-970 Campina Grande, Paraíba, Brazil email henrique@mat.ufcg.edu.br
*
✉henrique@mat.ufcg.edu.br
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Abstract

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We apply a mean-value inequality for positive subsolutions of the $f$-heat operator, obtained from a Sobolev embedding, to prove a nonexistence result concerning complete noncompact $f$-maximal spacelike hypersurfaces in a class of weighted Lorentzian manifolds. Furthermore, we establish a new Calabi–Bernstein result for complete noncompact maximal spacelike hypersurfaces in a Lorentzian product space.

Keywords

weighted Lorentzian product spaceBakry–Émery–Ricci tensorf-Laplacianf-maximal spacelike hypersurfaceentire spacelike graph

MSC classification

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Secondary: 53A07: Higher-dimensional and -codimensional surfaces in Euclidean $n$-space 35P15: Estimation of eigenvalues, upper and lower bounds
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 2 , October 2017 , pp. 317 - 325
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

The second author is partially supported by CNPq, Brazil, grant 303977/2015-9.

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