Supplement on curved flats in the space of point pairs and isothermic surfaces: A quaternionic calculus.
Hertrich-Jeromin, Udo (1997)
Documenta Mathematica
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Displaying similar documents to “Remarks on the Darboux transform of isothermic surfaces.”
Supplement on curved flats in the space of point pairs and isothermic surfaces: A quaternionic calculus.
Complex timelike isothermic surfaces and their geometric transformations.
Dussan, Martha, Magid, Martin (2006)
Balkan Journal of Geometry and its Applications (BJGA)
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The PDE describing constant mean curvature surfaces
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.
Minimizing the squared mean curvature integral for surfaces in space forms.
Hsu, Lucas, Kusner, Rob, Sullivan, John (1992)
Experimental Mathematics
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On some generalisations of constant mean curvature surfaces.
Fujioka, A., Inoguchi, J. (1999)
Lobachevskii Journal of Mathematics
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Polynomial translation surfaces of Weingarten types in Euclidean 3-space
Dae Yoon (2010)
Open Mathematics
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In this paper, we classify polynomial translation surfaces in Euclidean 3-space satisfying the Jacobi condition with respect to the Gaussian curvature, the mean curvature and the second Gaussian curvature.
Compact constant mean curvature surfaces with low genus.
Große-Brauckmann, Karsten, Polthier, Konrad (1997)
Experimental Mathematics
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Darboux transforms of Dupin surfaces
Emilio Musso, Lorenzo Nicolodi (2002)
Banach Center Publications
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We present a Möbius invariant construction of the Darboux transformation for isothermic surfaces by the method of moving frames and use it to give a complete classification of the Darboux transforms of Dupin surfaces.
Invariants and Bonnet-type theorem for surfaces in ℝ4
Georgi Ganchev, Velichka Milousheva (2010)
Open Mathematics
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In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...
On the Regularity of Alexandrov Surfaces with Curvature Bounded Below
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.