New constant mean curvature surfaces.
Kilian, Martin, McIntosh, Ian, Schmitt, Nicholas (2000)
Experimental Mathematics
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Kilian, Martin, McIntosh, Ian, Schmitt, Nicholas (2000)
Experimental Mathematics
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Michael T. Anderson, Lucio Rodriguez (1989)
Mathematische Annalen
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Luigi Ambrosio, Jérôme Bertrand (2016)
Analysis and Geometry in Metric Spaces
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In this note, we prove that on a surface with Alexandrov’s curvature bounded below, the distance derives from a Riemannian metric whose components, for any p ∈ [1, 2), locally belong to W1,p out of a discrete singular set. This result is based on Reshetnyak’s work on the more general class of surfaces with bounded integral curvature.
Alf Jonsson (1991)
Manuscripta mathematica
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Alain Joets (2008)
Banach Center Publications
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When drawing regular surfaces, one creates a concrete and visual example of a projection between two spaces of dimension 2. The singularities of the projection define the apparent contour of the surface. As a result there are two types of generic singularities: fold and cusp (Whitney singularities). The case of singular surfaces is much more complex. A priori, it is expected that new singularities may appear, resulting from the "interaction" between the singularities of the surface and...
Hsu, Lucas, Kusner, Rob, Sullivan, John (1992)
Experimental Mathematics
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Nikolaos Kapouleas (1995)
Inventiones mathematicae
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Colding, Tobias H., Kleiner, Bruce (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Hongyou Wu (2001)
Mathematica Bohemica
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We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.