A remark on the curvature of non-plane curves
Stanisław Gołąb, A. Pliś (1962)
Colloquium Mathematicae
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Displaying similar documents to “On Barbier's theorem”
A remark on the curvature of non-plane curves
Parallelograms inscribed in a curve having a circle as π/2-isoptic
Andrzej Miernowski (2008)
Annales UMCS, Mathematica
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Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.
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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Non-parametric convex hypersurfaces with a curvature restriction
Rolf Schneider (1983)
Annales Polonici Mathematici
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Counterexample to the convexity of level sets of solutions to the mean curvature equation
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.
Singularity structure in mean curvature flow of mean-convex sets.
Colding, Tobias H., Kleiner, Bruce (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Curvature contents of geometric spaces.
Lohkamp, Joachim (1998)
Documenta Mathematica
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Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature
Julià Cufí, Agustí Reventós (2014)
Archivum Mathematicum
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We relate the total curvature and the isoperimetric deficit of a curve in a two-dimensional space of constant curvature with the area enclosed by the evolute of . We provide also a Gauss-Bonnet theorem for a special class of evolutes.