Displaying similar documents to “The PDE describing constant mean curvature surfaces”

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.

Metric minimizing surfaces.

Petrunin, Anton (1999)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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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...