Minimal cones and the spherical Bernstein problem, II.
Wu-Yi Hsiang (1983)
Inventiones mathematicae
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Wu-Yi Hsiang (1983)
Inventiones mathematicae
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E. BOMBIERI, E. DE GIORGI, E. GIUSTI (1969)
Inventiones mathematicae
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Lin Jiu, Huafei Sun (2007)
Colloquium Mathematicae
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We give a classification of minimal homothetical hypersurfaces in an (n+1)-dimensional Euclidean space. In fact, when n ≥ 3, a minimal homothetical hypersurface is a hyperplane, a quadratic cone, a cylinder on a quadratic cone or a cylinder on a helicoid.
L. Simon, B. Solomon (1986)
Inventiones mathematicae
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Qi-Ming Wang (1994)
Mathematische Annalen
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Reiko Naka-Miyaoka (1980)
Mathematische Zeitschrift
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Bruce Solomon (1986)
Commentarii mathematici Helvetici
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Frank Morgan (1989)
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Claire C. Chan (1997)
Journal für die reine und angewandte Mathematik
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Toshiaki Adachi, Sadahiro Maeda (2006)
Colloquium Mathematicae
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We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.
Guido De Philippis, Emanuele Paolini (2009)
Rendiconti del Seminario Matematico della Università di Padova
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Francescopaolo Montefalcone (2016)
Analysis and Geometry in Metric Spaces
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In this paper, we generalize to sub-Riemannian Carnot groups some classical results in the theory of minimal submanifolds. Our main results are for step 2 Carnot groups. In this case, we will prove the convex hull property and some “exclosure theorems” for H-minimal hypersurfaces of class C2 satisfying a Hörmander-type condition.
Perdomo, Oscar (2002)
Revista Colombiana de Matemáticas
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