Displaying similar documents to “The Schwarz Lemma for nonpositively curved riemannian surfaces.”

Estimations of the best constant involving the L norm in Wente's inequality and compact H-surfaces in Euclidean space

Ge Yuxin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In the first part of this paper, we study the best constant involving the L norm in Wente's inequality. We prove that this best constant is universal for any Riemannian surface with boundary, or respectively, for any Riemannian surface without boundary. The second part concerns the study of critical points of the associate energy functional, whose Euler equation corresponds to H-surfaces. We will establish the existence of a non-trivial critical point for a plan domain with small holes....

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.