Immersed surfaces with constant curvature near infinity
David D. Bleecker (1978)
Compositio Mathematica
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Displaying similar documents to “An equality for the curvature function of a simple and closed curve on the plane.”
Immersed surfaces with constant curvature near infinity
A remark on the curvature of non-plane curves
Stanisław Gołąb, A. Pliś (1962)
Colloquium Mathematicae
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Computational studies of conserved mean-curvature flow
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...
Notes on geometry
Heinrich W. Guggenheimer (1969)
Archivum Mathematicum
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Total curvature of non-differentiable curves.
Gustavo Corach, Horacio Porta (1987)
Revista Matemática Iberoamericana
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On the total curvature of a closed curve
M. Rochowski (1969)
Annales Polonici Mathematici
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Overdetermined problems and the -Laplacian.
Kawohl, Bernd (2007)
Acta Mathematica Universitatis Comenianae. New Series
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Metrics of constant curvature on a Riemann surface with two corners on the boundary
Jürgen Jost, Guofang Wang, Chunqin Zhou (2009)
Annales de l'I.H.P. Analyse non linéaire
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Structurally stable configurations of lines of mean curvature and umbilic points on surfaces immersed in R.
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...