Access the full text.
Sign up today, get DeepDyve free for 14 days.
ST Yau (1975)
Harmonic functions on complete Riemannian manifoldsCommun. Pure Appl. Math., 28
C. Aquino, H. Lima (2014)
On the Unicity of Complete Hypersurfaces Immersed in a Semi-Riemannian Warped ProductThe Journal of Geometric Analysis, 24
Alma Albujer, L. Alías (2007)
Calabi–Bernstein results for maximal surfaces in Lorentzian product spacesJournal of Geometry and Physics, 59
L. Alías, A. Romero, Miguel Caja (1997)
SPACELIKE HYPERSURFACES OF CONSTANT MEAN CURVATURE AND CALABI-BERNSTEIN TYPE PROBLEMSTohoku Mathematical Journal, 49
C. Aquino, H. Lima, E. Lima (2015)
Complete CMC spacelike hypersurfaces immersed in a Lorentzian product spaceArchiv der Mathematik, 104
C. Aquino, H. Lima, E. Lima (2014)
On the angle of complete CMC hypersurfaces in Riemannian product spacesDifferential Geometry and Its Applications, 33
H. Lima, J. Lima (2012)
Complete hypersurfaces immersed in a semi-Riemannian warped productDifferential Geometry and Its Applications, 30
João Barbosa, A. Colares (1997)
Stability of Hypersurfaces with Constant $$r$$ -Mean CurvatureAnnals of Global Analysis and Geometry, 15
K. Tenenblat (1971)
On isometric immersions of riemannian manifoldsBoletim da Sociedade Brasileira de Matemática, 2
Alma Albujer, F. Camargo, H. Lima (2011)
Complete spacelike hypersurfaces in a Robertson–Walker spacetimeMathematical Proceedings of the Cambridge Philosophical Society, 151
L. Alías, A. Romero, Miguel Caja (1995)
Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimesGeneral Relativity and Gravitation, 27
LJ Alías, A Romero, M Sánchez (1997)
Spacelike hypersurfaces of constant mean curvature and Calabi–Bernstein type problemsTôhoku Math. J., 49
L. Alías, Debora Impera, M. Rigoli (2011)
Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson–Walker spacetimesMathematical Proceedings of the Cambridge Philosophical Society, 152
I. Salavessa (2006)
Spacelike graphs with parallel mean curvatureBulletin of The Belgian Mathematical Society-simon Stevin, 15
A. Caminha, H. Lima (2008)
Complete spacelike hypersurfaces in conformally stationary Lorentz manifoldsGeneral Relativity and Gravitation, 41
H Omori (1967)
Isometric immersions of Riemannian manifoldsJ. Math. Soc. Jpn., 19
H. Rosenberg (1993)
Hypersurfaces of constant curvature in space formsBulletin Des Sciences Mathematiques, 117
L. Alías, A. Colares, H. Lima (2013)
On the rigidity of complete spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetimeBulletin of the Brazilian Mathematical Society, New Series, 44
L. Alías, Debora Impera, M. Rigoli (2011)
Hypersurfaces of constant higher order mean curvature in warped productsTransactions of the American Mathematical Society, 365
Guanghan Li, I. Salavessa (2008)
Graphic Bernstein results in curved pseudo-Riemannian manifoldsJournal of Geometry and Physics, 59
H. Lima, E. Lima (2014)
Generalized maximum principles and the unicity of complete spacelike hypersurfaces immersed in a Lorentzian product spaceBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 55
C. Aquino, H. Lima (2011)
UNIQUENESS OF COMPLETE HYPERSURFACES WITH BOUNDED HIGHER ORDER MEAN CURVATURES IN SEMI-RIEMANNIAN WARPED PRODUCTSGlasgow Mathematical Journal, 54
B. O'neill (1983)
Semi-Riemannian Geometry With Applications to Relativity
C. Aquino, H. Lima (2011)
On the rigidity of constant mean curvature complete vertical graphs in warped productsDifferential Geometry and Its Applications, 29
The purpose of this article is to study the uniqueness of complete hypersurfaces satisfying some pinching curvature condition. Here, we use the generalized maximum principle of Omori–Yau to obtain uniqueness results for complete spacelike hypersurfaces immersed in a Lorentzian product space. In addition, we obtain the analogue results for complete hypersurfaces immersed in a Riemannian product space.
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Jun 2, 2017
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.