Titlebook: Reshetnyak‘s Theory of Subharmonic Metrics; François Fillastre,Dmitriy Slutskiy Book 2023 The Editor(s) (if applicable) and The Author(s),

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Arc Length in Manifolds of Bounded Curvature with an Isothermal Metric,etrized manifolds, whose metric in a neighborhood of any point is given by an isothermal linear element .(.)(d. + d.), where the function . is the exponential of the difference of two subharmonic functions.

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he complete proofs of Reshetnyak‘s theorem on the subject.It.Despite the fundamental role played by Reshetnyak‘s work in the theory of surfaces of bounded integral curvature, the proofs of his results were only available in his original articles, written in Russian and often hard to find. This situa