Many classical univalence criteria depending on the Schwarzian derivative are special cases of a result, proved in [18], involving both conformal mappings and conformal metrics. The classical theorems for analytic functions on the disk emerge by choosing appropriate conformal metrics and computing a generalized Schwarzian. The results in this paper address questions of extending functions which...

The conformal geometry of the Schwarzian Davey-Stewartson II hierarchy and its discrete analogue is investigated. Connections with discrete and continuous isothermic surfaces and generalised Clifford configurations are recorded. An interpretation of the Schwarzian Davey-Stewartson II flows as integrable deformations of conformally immersed surfaces is given.

Two derivative Jackiw Teitelboim gravity theory captures the near horizon dynamics of higher dimensional extremal black holes, which is governed by a Schwarzian action at boundary in region. The partition function corresponding to this correctly gives statistical entropy hole. In paper, we study thermodynamics spherically symmetric four holes presence arbitrary perturbative corrections. We find...

If \(\Omega\) is a simply connected domain in \(\overline{\mathbf C}\) then, according to the Ahlfors-Gehring theorem, quasidisk if and only there exists sufficient condition for univalence of holomorphic functions relation growth their Schwarzian derivative. We extend this theorem harmonic mappings by proving criterion on quasidisks. also show that satisfying admit homeomorphic extension and, ...

We prove that if V n is a Chebyshev system on the circle and f(x) is a continuous function with at least n + 1 sign changes then there exists an orientation preserving diffeomorphism of S that takes f to a function L-orthogonal to V . We also prove that if f(x) is a function on the real projective line with at least four sign changes then there exists an orientation preserving diffeomorphism of...

TO THE RIEMANN MAP Zheng-Xu He and Oded Schramm Abstract. Let $ C be a simply connected domain. The Rodin-SullivanTheorem states that a sequence of disk packings in the unit disk U converges, in a well de ned sense, to a conformal map from to U . Moreover, it is known that the rst and second derivatives converge as well. Here, it is proven that for hexagonal disk packings the convergence is C1 ...