On the Regularity of Surfaces with Prescribed Mean Curvature at a Free Boundary.
Willi Jäger, Stefan Hildebrandt (1970)
Mathematische Zeitschrift
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Willi Jäger, Stefan Hildebrandt (1970)
Mathematische Zeitschrift
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Alessandro Carlotto (2019)
Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche
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We present a wide-spectrum overview of some recent developments in the theory of free boundary minimal surfaces, with special emphasis on the problem of compactness under mild curvature conditions on the ambient manifold.
Kilian, Martin, McIntosh, Ian, Schmitt, Nicholas (2000)
Experimental Mathematics
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Stefan Hildebrandt (1972)
Mathematische Zeitschrift
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Maria Athanassenas (1987)
Journal für die reine und angewandte Mathematik
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Klaus Ecker (1982)
Mathematische Zeitschrift
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Ildefonso Castro Lopez, Manuel Ritore (1991)
Séminaire de théorie spectrale et géométrie
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Klaus Steffen (1976)
Mathematische Zeitschrift
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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.
Claus Gerhardt (1974)
Mathematische Zeitschrift
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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.