The modulus of a family of curves on an abstract surface over a spherical ring
Keywords:
abstract surface, modulus of a curve family, spherical ring.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 the point depends on the direction of movement along the curve; additionally, the volume element is generated by some weight function.
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Published
2020-11-10
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Real, complex and functional analysis