Curvature contents of geometric spaces.
Lohkamp, Joachim (1998)
Documenta Mathematica
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Lohkamp, Joachim (1998)
Documenta Mathematica
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Brent Collins (2001)
Visual Mathematics
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Iyigün, Esen (2002)
APPS. Applied Sciences
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Haesen, Stefan, Verpoort, Steven (2010)
Beiträge zur Algebra und Geometrie
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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.
Eduardo H. A. Gonzales, Umberto Massari, Italo Tamanini (1993)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The existence of a singular curve in is proven, whose curvature can be extended to an function. The curve is the boundary of a two dimensional set, minimizing the length plus the integral over the set of the extension of the curvature. The existence of such a curve was conjectured by E. De Giorgi, during a conference held in Trento in July 1992.
Christos Baikoussis, Themis Koufogiorgos (1988)
Colloquium Mathematicae
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Rolf J. Ryham (2016)
Molecular Based Mathematical Biology
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A continuum mechanical model based on the Helfrich Hamiltonian is devised to investigate the coupling between lipid composition and membrane curvature. Each monolayer in the bilayer is modeled as a freely deformable surface with a director field for lipid orientation. A scalar field for the mole fraction of two lipid types accounts for local changes in composition. It allows lipids to access monolayer regions favorable to their intrinsic curvature at the expense of increasing entropic...
Wolfgang Kühnel (1979)
Colloquium Mathematicae
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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...
Frederick Wilhlem (1995)
Mathematische Zeitschrift
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Jiangguo Liu, Farrah Sadre-Marandi, Simon Tavener, Chaoping Chen (2015)
Molecular Based Mathematical Biology
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It is known that the retrovirus capsids possess a fullerene-like structure. These caged polyhedral arrangements are built entirely from hexagons and exactly 12 pentagons according to the Euler theorem. Viral capsids are composed of capsid proteins, which create the hexagon and pentagon shapes by groups of six (hexamer) and five (pentamer) proteins. Different distributions of these 12 pentamers result in icosahedral, tubular, or conical shaped capsids. These pentamer clusters introduce...
H.B., Jr Lawson, M.-L. Michelsohn (1984)
Inventiones mathematicae
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