Geodesic
The modulus of a family of curves on an abstract surface over a spherical ring
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1816-1822

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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. 
@article{SEMR_2020_17_a141,
     author = {M. V. Tryamkin},
     title = {The modulus of a family of curves on an abstract surface over a spherical ring},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1816--1822},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a141/}
}
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M. V. Tryamkin. The modulus of a family of curves on an abstract surface over a spherical ring. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1816-1822. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a141/