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math.CV2023
On the Conformal Energy of Quasisymmetric and Quasimöbius Mappings
Mihai Florincescu, Gaven Martin
This article identifies the conformal energy (or mean distortion) of extremal mappings of finite distortion with a given quasisymmetric mapping of the circle as boundary data. The…
math.AP2023
Topological regularity for solutions to the generalised Hopf equation
Gaven Martin, Cong Yao
The generalised Hopf equation is the first order nonlinear equation with data a holomorphic functions and a positive weight, \[ h_w\,\overline{h_\wbar}\,η(w) = Φ.\] T…
math.CV2023
The Generic Failure of Lower-semicontinuity for the Linear Distortion Functional
Sayed Mohsen Hashemi, Gaven J. Martin
We consider the convexity properties of distortion functionals, particularly the linear distortion, defined for homeomorphisms of domains in Euclidean -spaces, . The in…