Constant mean curvature tori in terms of elliptic functions.
U. Abresch (1987)
Journal für die reine und angewandte Mathematik
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U. Abresch (1987)
Journal für die reine und angewandte Mathematik
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Publications de l'Institut Mathématique. Nouvelle Série
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Xu-Jia Wang (2014)
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The convexity of level sets of solutions to the mean curvature equation is a long standing open problem. In this paper we give a counterexample to it.
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In this paper we establish a Liouville type theorem for fully nonlinear elliptic equations related to a conjecture of De Giorgi in . We prove that if the level lines of a solution have bounded curvature, then these level lines are straight lines. As a consequence, the solution is one-dimensional. The method also provides a result on free boundary problems of Serrin type.
Ronaldo García, Jorge Sotomayor (2001)
Publicacions Matemàtiques
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In this paper we study the pairs of orthogonal foliations on oriented surfaces immersed in R whose singularities and leaves are, respectively, the umbilic points and the lines of normal mean curvature of the immersion. Along these lines the immersions bend in R according to their normal mean curvature. By analogy with the closely related Principal Curvature Configurations studied in [S-G], [GS2], whose lines produce the extremal for the immersion, the pair of foliations by lines of...
H.B., Jr Lawson, M.-L. Michelsohn (1984)
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Wolfgang Kühnel (1979)
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