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Chapitre D'ouvrage Année : 2023

An introduction to Reshetnyak's theory of subharmonic distances

Résumé

The aim of the present text is to provide some basics around Reshetnyak’s theory of subharmonic distances, together with an overview of the main results. This text is intended to be a complement to the English translation of [Reshetnyak, 1954], [Reshetnyak, 1959], [Reshetnyak, 1960a], [Reshetnyak, 1960b], [Reshetnyak, 1961b], [Reshetnyak, 1961a], [Reshetnyak, 1962], [Reshetnyak, 1963a], [Reshetnyak, 1963b] and [Huber, 1960]. They all will be published in a same volume [Fillastre and Slutskiy, 2021]. While subharmonic distances are often confused with distances of bounded curvature, we present them as a complete autonomous theory. In turn, there is no specific prerequisite for the present text.

Dates et versions

hal-03798763 , version 1 (05-10-2022)

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François Fillastre. An introduction to Reshetnyak's theory of subharmonic distances. Reshetnyak's Theory of Subharmonic Metrics, Springer International Publishing, pp.47-145, 2023, ⟨10.1007/978-3-031-24255-7_4⟩. ⟨hal-03798763⟩
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