In this paper we revisit the construction of supersymmetric Schwarzians using nonlinear realizations. We show that ${\cal N}=0,1,2,3,4$ can be systematically obtained as certain projections Maurer-Cartan forms superconformal groups after imposing simple conditions on them. also present Schwarzian actions defined integrals products Cartan forms. contrast with previous attempts to obtain super-Sc...

Let f be a sense-preserving harmonic mapping in the unit disk. We give a sufficient condition in terms of the pre-Schwarzian derivative of f to ensure that it can be extended to a quasiconformal map in the complex plane. Introduction A well-known criterion due to Becker [5] states that if a locally univalent analytic function φ in the unit disk D satisfies (1) sup z∈D ∣∣∣∣φ′′(z) φ′(z) ∣∣∣∣ (1− ...

Differential equations are derived for a continous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.

Let A be entire. Suppose that there exists an unbounded quasidisk D such that A is sufficiently small in D. We prove that then any nontrivial solution to y" + Ay = 0 has at most one zero in D. We show that if A = Q exp P where P and Q are polynomials, one can usually take D to be an angle of opening x/n where n is the degree of P .

A holomorphic quadratic differential on a hyperbolic Riemann surface has an associated measured foliation, which can be straightened to yield a measured geodesic lamination. On the other hand, a quadratic differential can be considered as the Schwarzian derivative of a CP1 structure, to which one can naturally associate another measured geodesic lamination (using grafting). We compare these two...

We extend the notion of a Thomas projective connection (a projective equivalence class of linear connections) for supermanifolds. As a by-product, we arrive at a generalisation of the multidimensional Schwarzian derivative for the super case which was previously unknown. This is combined with our previous construction of a Laplacian on the algebra of densities for a projectively connected manif...

The main character of the present note is the Schwarzian derivative, and we start with a brief reminder of its definition and main properties. Let f : RP → RP be a projective line diffeomorphism. For every point x ∈ RP there exists a unique projective transformation gx : RP 1 → RP whose 2-jet at x coincides with that of f . The Schwarzian derivative S(f) measures the deviation of the 3-jet jf f...