For $$-1\le B<A\le 1$$ , let $${\mathcal {S}}^*(A,B)$$ denote the class of Janowski starlike functions that satisfy subordination relation $$zf'(z)/f(z)\prec (1+Az)/(1+Bz)$$ . In present article, we determine sharp estimate pre-Schwarzian norm for in

It was recently demonstrated that N=1,2,3,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realisations to finite-dimensional superconformal groups OSp(1|2), SU(1,1|1), OSp(3|2), SU(1,1|2), respectively, thus avoiding use field theory techniques. In this work, a similar construction is applied exceptional supergroup D(2,1;a), which describes most general N=4...

and that the Schwarzian is identically zero exactly for Möbius transformations. Let D denote the unit disk. There has been progress in several areas, but the innovations we treat here come primarily from an injectivity criterion for conformal, local diffeomorphisms of an n-dimensional Riemannian manifold into the n-sphere. The criterion involves a generalization of the Schwarzian derivative whi...

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.

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means subordination, analytic parts which are reciprocal starlike (or convex) functions. Further, combining graph function, discuss bound Bloch constant and norm pre-Schwarzian derivative for classes.

We consider two theorems formulated in the derivation of the Quantum Hamilton–Jacobi Equation from the EP. The first one concerns the proof that the cocycle condition uniquely defines the Schwarzian derivative. This is equivalent to show that the infinitesimal variation of the stress tensor “exponentiates” to the Schwarzian derivative. The cocycle condition naturally defines the higher dimensio...

A meromorphic projective structure on a punctured Riemann surface X∖P is determined, after fixing standard X, by quadratic differential with poles of order three or more at each puncture in P. In this article we prove the analogue Thurston's grafting theorem for such structures, that involves crowned hyperbolic surfaces. This also provides description structures C have polynomial Schwarzian der...