We study conformal mappings in the Grushin plane and provide a number of their characterizations in terms of Sobolev mappings and their geometry. Furthermore, we connect conformality on the Grushin plane with conformality on the complex plane by using the canonical quasisymmetry between the α–Grushin plane and the complex plane. Among applications, we discuss admissible curves and length-distortion estimates in the Grushin plane, as well as the Carathéodory extension theorem.
No takes yet. Share an insight, caveat, or question.
Marcin Walicki (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: