Geodesic
Equicontinuity of homeomorphisms with unbounded characteristic
Matematičeskie trudy, Tome 15 (2012) no. 1, pp. 178-204

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The article is devoted to the study of the boundary properties of homeomorphisms $f\colon D\to D'$, $D,D'\subset\mathbb R^n$, satisfying some geometric conditions responsible for the control of the measure of distortion of families of curves in $D$. Under additional requirements on the boundaries $\partial D$ and $\partial D'$ of the domains, we prove that the family of all such homeomorphisms is equicontinuous in $\overline D$. 
@article{MT_2012_15_1_a10,
     author = {E. A. Sevostyanov},
     title = {Equicontinuity of homeomorphisms with unbounded characteristic},
     journal = {Matemati\v{c}eskie trudy},
     pages = {178--204},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2012_15_1_a10/}
}
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E. A. Sevostyanov. Equicontinuity of homeomorphisms with unbounded characteristic. Matematičeskie trudy, Tome 15 (2012) no. 1, pp. 178-204. http://geodesic.mathdoc.fr/item/MT_2012_15_1_a10/