This article is cited in 3 papers

Real, complex and functional analysis

The modulus of a family of curves on an abstract surface over a spherical ring

M. V. Tryamkin

Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia

Abstract: We obtain a two-sided estimate for the modulus of the family of all locally rectifiable curves joining two concentric spheres on a so-called abstract surface. The last notion means that, for a given curve and a point on it, the length element of the curve at this point depends on the direction of movement along the curve; in addition, the volume element is generated by some weight function.

Keywords: abstract surface, modulus of a family of curves, spherical ring.

UDC: 517.5

MSC: 30C65

Received September 1, 2020, published November 10, 2020

Language: English

DOI: 10.33048/semi.2020.17.123

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