Pierluigi Benevieri, João Marcos do Ó, Everaldo Souto de Medeiros (2007)
Banach Center Publications
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We give an existence result for a periodic boundary value problem involving mean curvature-like operators. Following a recent work of R. Manásevich and J. Mawhin, we use an approach based on the Leray-Schauder degree.
Roman Boutellier (1981)
Mathematische Zeitschrift
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Robert Gulliver (1973/74)
Manuscripta mathematica
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Lohkamp, Joachim (1998)
Documenta Mathematica
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Brent Collins (2001)
Visual Mathematics
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Luo, Feng (2005)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Haesen, Stefan, Verpoort, Steven (2010)
Beiträge zur Algebra und Geometrie
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Christos Baikoussis, Themis Koufogiorgos (1988)
Colloquium Mathematicae
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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.
Iyigün, Esen (2002)
APPS. Applied Sciences
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Wolfgang Kühnel (1979)
Colloquium Mathematicae
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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.
H.B., Jr Lawson, M.-L. Michelsohn (1984)
Inventiones mathematicae
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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...