Arc Length in Manifolds of Bounded Curvature with an Isothermal Metric

Yu. G. Yu.G. ()
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Yu. G. Yu.G.: Sobolev Institute of Mathematics

Chapter Chapter 12 in Reshetnyak's Theory of Subharmonic Metrics, 2023, pp 283-298 from Springer

Abstract: Abstract The notion of two-dimensional manifolds of bounded curvature was introduced by A. D. Alexandrov in the articles [1, 2]. The author of this chapter established in the articles [5] (Chap. 5 ), [6] (Chap. 7 ), and [7] (Chap. 8 ) that manifolds of bounded curvature can be characterized as two-dimensional metrized manifolds, whose metric in a neighborhood of any point is given by an isothermal linear element λ(z)(du2 + dv2), where the function λ is the exponential of the difference of two subharmonic functions.

Date: 2023
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DOI: 10.1007/978-3-031-24255-7_12

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