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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Henri Anciaux (2002-2003)
Séminaire de théorie spectrale et géométrie
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Benz, Walter (2000)
Beiträge zur Algebra und Geometrie
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Fujioka, A., Inoguchi, J. (1999)
Lobachevskii Journal of Mathematics
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Roberta Alessandroni (2008-2009)
Séminaire de théorie spectrale et géométrie
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This is a short overview on the most classical results on mean curvature flow as a flow of smooth hypersurfaces. First of all we define the mean curvature flow as a quasilinear parabolic equation and give some easy examples of evolution. Then we consider the M.C.F. on convex surfaces and sketch the proof of the convergence to a round point. Some interesting results on the M.C.F. for entire graphs are also mentioned. In particular when we consider the case of dimension one, we can compute...
Große-Brauckmann, Karsten, Polthier, Konrad (1997)
Experimental Mathematics
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Miroslav Kolář, Michal Beneš, Daniel Ševčovič (2014)
Mathematica Bohemica
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The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational...
Chopp, David L., Sethian, James A. (1993)
Experimental Mathematics
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Atsushi Imiya (2013)
Actes des rencontres du CIRM
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We first define the curvature indices of vertices of digital objects. Second, using these indices, we define the principal normal vectors of digital curves and surfaces. These definitions allow us to derive the Gauss-Bonnet theorem for digital objects. Third, we introduce curvature flow for isothetic polytopes defined in a digital space.
David D. Bleecker (1978)
Compositio Mathematica
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