Curvature contents of geometric spaces.

Lohkamp, Joachim

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A note on $(n - r)$ -curvature planes.

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The mean curvature of the second fundamental form of a hypersurface.

Haesen, Stefan, Verpoort, Steven (2010)

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A lower bound for the i-th total absolute curvature of an immersion

Wolfgang Kühnel (1979)

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Ovaloids with prescribed curvature of the second fundamental form

Christos Baikoussis, Themis Koufogiorgos (1988)

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On continuous mappings between non-negatively and non-positively curved manifolds.

Paweł Grzegorz Walczak (1984)

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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.

Curvature Concentrations on the HIV-1 Capsid

Jiangguo Liu, Farrah Sadre-Marandi, Simon Tavener, Chaoping Chen (2015)

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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...

Spaces with Ricci curvature bounds.

Colding, Tobias H. (1998)

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Embedding and surrounding with positive mean curvature.

H.B., Jr Lawson, M.-L. Michelsohn (1984)

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On radius, systole, and positive Ricci curvature.

Frederick Wilhlem (1995)

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Characterizations of the sphere by the curvature of the second fundamental form

Thomas Hasanis (1982)

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On Tori with Parallel Mean Curvature Vector in a Space of Constant Curvature.

Katsuei Kenmotsu (1974)

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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...