Mappings with Finite Length Distortion and Prime Ends on Riemann Surfaces
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DOI: 10.1007/s10958-020-04869-z
Abstract: Abstract The present paper is a continuation of our research that was devoted to the theory of the boundary behavior of mappings in the Sobolev classes (mappings with generalized derivatives) on Riemann surfaces. Here we… read more here.
Keywords: length distortion; prime ends; mappings finite; finite length ... See more keywords
Prime ends in the Heisenberg group H_1 and the boundary behavior of quasiconformal mappings
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DOI: 10.5186/aasfm.2018.4342
Abstract: We investigate prime ends in the Heisenberg group $\mathbb{H}_{1}$ extending N\"akki's construction for collared domains in Euclidean spaces. The corresponding class of domains is defined via uniform domains and the Loewner property. Using prime ends… read more here.
Keywords: prime ends; heisenberg group; group boundary; quasiconformal mappings ... See more keywords
On boundary extension of mappings in metric spaces in the terms of prime ends
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DOI: 10.5186/aasfm.2019.4405
Abstract: We study the boundary behavior of the so-called ring $Q$-mappings obtained as a natural generalization of mappings with bounded distortion. We establish a series of conditions imposed on a function $Q(x)$ for the continuous extension… read more here.
Keywords: mappings metric; boundary extension; metric spaces; prime ends ... See more keywords