A singular example for the averaged mean curvature flow.
Mayer, Uwe F. (2001)
Experimental Mathematics
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Mayer, Uwe F. (2001)
Experimental Mathematics
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Xu-Jia Wang (2014)
Journal of the European Mathematical Society
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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.
Haesen, Stefan, Verpoort, Steven (2010)
Beiträge zur Algebra und Geometrie
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Rolf Schneider (1983)
Annales Polonici Mathematici
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Giuseppe Pipoli (2017)
Complex Manifolds
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In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces. We show similarities and differences between the case considered, with particular attention to how the geometry of the ambient manifolds influences the behaviour of the evolution. Moreover we try, when possible, to give an unified approach to the results present in literature.
W. Cieslak, S. Gozdz (1990)
Matematički Vesnik
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Lohkamp, Joachim (1998)
Documenta Mathematica
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Gerhard Huisken (1987)
Journal für die reine und angewandte Mathematik
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Brent Collins (2001)
Visual Mathematics
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Stefano Amato, Giovanni Bellettini, Lucia Tealdi (2015)
Geometric Flows
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Given an anisotropy ɸ on R3, we discuss the relations between the ɸ-calibrability of a facet F ⊂ ∂E of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet ̃︀ BFɸ of the unit ball of ɸ, ɸ-calibrability is equivalent to show the existence of a ɸ-subunitary vector field in F, with suitable normal trace on @F, and with constant divergence equal to the ɸ-mean curvature of F. Assuming E convex at F, ̃︀ BFɸ a disk, and F (strictly) ɸ-calibrable,...
Theodora Bourni, Mat Langford (2016)
Geometric Flows
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We show that any strictly mean convex translator of dimension n ≥ 3 which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a consequence, we deduce that any translating solution of the mean curvature flow which arises as a blow-up limit of a two-convex mean curvature flow of compact immersed hypersurfaces of dimension n ≥ 3 is rotationally symmetric. The proof is rather robust, and applies to a more general class of translator equations....
Nobumitsu Nakauchi (1993)
Manuscripta mathematica
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A. Szybiak (1964)
Annales Polonici Mathematici
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