arXiv:2611.14792v1 Announce Type: new Abstract: We consider mappings between domains of two Riemannian surfaces. The main subject of the investigation are families of homeomorphisms with moduli inequalities. For such families, we obtain the uniform openness (uniform lightness). As a consequence, we obtain similar results for homeomorphisms of Sobolev classes with finite distortion whenever its maximal dilatations have a majorant integrable on almost all concentric circles. In particular, we obtain the Koebe-type theorem for both direct and inverse Sobolev mappings.
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