Abstract
In this paper, we provided conditions for an entire constant mean curvature Killing graph lying inside a possible unbounded region to be necessarily a slice.
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Bombieri, E., de Giorgi, E., Miranda, M.: Una maggiorazione a priori relativa alle ipersuperfici minimali non parametriche. Arch. Rational Mech. Anal. 32, 255–267 (1969)
Chern, S.S.: On the curvatures of a piece of hypersurfaces in Euclidean space. Abh. Math. Sem. Univ. Hamburg 29, 77–91 (1965)
Dajczer, M., Hinojosa, P., de Lira, J.H.: Killing graphs with prescribed mean curvature. Calc. Var. Partial Differ. Equ. 248, 231–248 (2008)
Dajczer, M., de Lira, J.H.: Entire bounded constant mean curvature Killing graphs. J. Math. Pures Appl. 103, 219–227 (2015)
Flanders, H.: Remark on mean curvature. J. Lond. Math. Soc. 41, 364–366 (1966)
Fornari, S., Ripoll, J.: Killing fields, mean curvature and translation maps. Ill. J. Math. 48, 1385–1403 (2004)
Korevaar, N.: An easy proof of the interior gradient bound for solutions to the prescribed mean curvature equation. Proc. Sympos. Pure Math. 45, 81–89 (1986)
Pigola, S., Rigoli, M., Setti, A.: Maximum principles on Riemannian manifolds and applications. Mem. Am. Math. Soc. 174 (2005)
Rosenberg, H., Schulze, F., Spruck, J.: The half-space property and entire positive minimal graphs in \(M\times {\mathbb{R}}\). J. Differ. Geom. 95, 321–336 (2013)
Saloff-Coste, L.: Uniformly elliptic operators on Riemannian manifolds. J. Differ. Geom. 36, 417–450 (1992)
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Dajczer, M., de Lira, J.H. Entire Unbounded Constant Mean Curvature Killing Graphs. Bull Braz Math Soc, New Series 48, 187–198 (2017). https://doi.org/10.1007/s00574-016-0019-3
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DOI: https://doi.org/10.1007/s00574-016-0019-3