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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费解

On Isoperimetric Property of Two-dimensional Manifolds with Curvature Bounded from Above by , that for each open set . ⊂ . . We use the following notation: . . Let us suppose that for each compact . ⊂ ., .(.) < . and there is . > 0 such that for . ∈ . and . < .: . Then in any open set . with closure contained in ., the function . can be written as: . where . is a harmonic function and . is a signed measure such that for any . ⊂ .

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胰脏

On the Potential Theoretic Aspect of Alexandrov Surface Theory,rs—amongst whom, most notably Wintner [.] and [.], Chern–Hartman–Wintner [.], and Reshetnyak [.] (Chap. .)—have sought to determine the weakest possible conditions under which the existence of such coordinate systems may be proven.

Pastry

How I Got Involved in Research on Two-Dimensional Manifolds of Bounded Curvature,In the thirties of the last century, a new bright figure appeared on the horizon of Soviet mathematics: Aleksandr Danilovich Alexandrov. He was an actively working young mathematician, a man with outstanding talent and bright temperament. He is the author of research on the theory of convex bodies, continuing the work of H. Minkowski.

凹室

Isothermal Coordinates on Manifolds of Bounded Curvature,The notion of two-dimensional manifolds of bounded curvature was introduced by A. D. Alexandrov in [.,.,.,.].

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Isothermal Coordinates on Manifolds of Bounded Curvature II, The present second part of the article is devoted to the proof of three basic lemmas stated in [.] (Chap. .). The definitions of the main notions and the terminology adopted in [.] (Chap. .) are supposed to be known in what follows.

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Turn of Curves in Manifolds of Bounded Curvature with Isothermal Metric,A. D. Alexandrov [., .] introduced an important class of metric spaces—two-dimensional manifolds of bounded curvature. The theory of these spaces was developed in detail by A. D. Alexandrov in cooperation with V. A. Zalgaller. The main results of this theory are explained in the monograph [.].

山羊

François Fillastre,Dmitriy SlutskiyThe articles of Yu. G. Reshetnyak about surfaces of bounded curvature accessible and translated.These articles are the only references for the complete proofs of Reshetnyak‘s theorem on the subject.It