Curvature contents of geometric spaces.
Lohkamp, Joachim (1998)
Documenta Mathematica
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Lohkamp, Joachim (1998)
Documenta Mathematica
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Haesen, Stefan, Verpoort, Steven (2010)
Beiträge zur Algebra und Geometrie
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Brent Collins (2001)
Visual Mathematics
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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.
E. Ossanna (1992)
Rendiconti del Seminario Matematico della Università di Padova
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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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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...
Dae Won Yoon, Yılmaz Tunçer, Murat Kemal Karacan (2013)
Annales Polonici Mathematici
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We study quadric surfaces in Euclidean 3-space with non-degenerate second fundamental form, and classify them in terms of the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature.
Iyigün, Esen (2002)
APPS. Applied Sciences
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H.B., Jr Lawson, M.-L. Michelsohn (1984)
Inventiones mathematicae
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Colding, Tobias H. (1998)
Documenta Mathematica
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