Caustic of the three-dimensional ellipsoid. (Caustique de la surface ellipsoïdale à trois dimensions.)
Joets, Alain, Ribotta, Roland (1999)
Experimental Mathematics
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Joets, Alain, Ribotta, Roland (1999)
Experimental Mathematics
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G. Lucca (2003)
Visual Mathematics
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Brakke, Kenneth A. (1992)
Experimental Mathematics
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Kobayashi, Shimpei (2004)
Balkan Journal of Geometry and its Applications (BJGA)
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Chris Peters (1995)
Cours de l'institut Fourier
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Martin Bright (2011)
Acta Arithmetica
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Balan, Vladimir, Vîlcea, Ştefania-Alina (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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G. Lucca (2004)
Visual Mathematics
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Günay Doğan, Ricardo H. Nochetto (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise...
Günay Doğan, Ricardo H. Nochetto (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise...
Teruo Nagase, Akiko Shima (2005)
Fundamenta Mathematicae
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Let Γ be a 4-chart with at most two crossings. We show that if the closure of the surface braid obtained from Γ is one 2-sphere, then the sphere is a ribbon surface.