The f-minimal submanifolds and a bernstein theorem in the space G2 x Rn
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Abstract
In this paper, we construct definitions of f-mean curvature vector and f-minimal sub-manifolds. Accordingly, we prove that a -minimal entire graph of a differential function reaching a critical point in the space G2 x Rn , n >= 1 must be a plane.
Keywords
Bernstein, density, mean curvature, entire graph, Lagrange.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
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[2]. M. Gromov (2003), “Isoperimetry of waists and concentration of maps”, Geom. Funct. Anal., No. 13, P. 178-215.
[3]. Th. Hasanis, A.S. Halila, and Th. Vlachos(2009), “Minimal graphs in with bounded Jacobians”,Proc. Amer. Math. Soc., 137, no. 10, P. 3463-3471.
[4]. D.T. Hieuand N.M. Hoang (2009), "Ruled minimal surfaces in with density ",Pacific Journal of Mathematics, 243, No. 2, P. 277-285.
[5]. D.T. Hieuand T.L. Nam (2014), "Bernstein type theorem for entire weighted minimal graphs in ", Journal of Geometry and Physics, 81, P. 89-91.
[6]. F. Morgan (2005), “Manifolds with density”, Notices Amer. Math. Soc., 52, P. 853-858.
[7]. F. Morgan (2006), “Myers Theorem with density”, Kodai Math. J., 29, P. 454-460.
[8]. F. Morgan (2009), “Manifolds with density and Perelman's proof of the Poincare Conjecture”, Amer. Math. Monthly, 116, P. 134-142.
[9]. R. Osserman (2002), A survey on minimal surfaces,Courier Dover Publications.
[10]. L. Wang (2011), “A Bernstein type theorem for self-similar shrinkers”, Geom. Dedicata, 151, P. 297-303.
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