grantor: University of TorontoLet 'D' be the unit disc in the complex plane, and lz=1 1-z2 the hyperbolic line element. Let S be the class of holomorphic functions &cubl0;f:D &rarrr;C&vbm0;f1-1, f0 =0,f' 0=1&cubr0; Define higher order Schwarzian derivatives by s3f= f'''f' -32 f''f' 2,s n+1f=sn f'- n-1f'' f'sn f We show that for any f∈S , snf zn-3n-2!l zn-1[for all]z∈ D . These bounds are sharp. We also give sharp two-point geometric distortion theorems for these in term of hyperbolic distance. Furthermore, we develop the calculus of the non-holomorphic derivatives of Minda and Peschl for conformal metrics, in order to facilitate function- theoretic computations. The relation of these derivatives to the...
Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and O...
This paper is a survey of some new techniques and new results on sufficient conditions in terms of t...
Let Ω and Π be two hyperbolic simply connected domains in the extended complex plane C̄ = C ∪ {∞}. W...
grantor: University of TorontoLet 'D' be the unit disc in the complex plane, and lz=1 1-...
Abstract. This paper shows how new dierential geometric ap-proaches to univalence criteria involving...
Abstract. Peschl defined invariant higher-order derivatives of a holomorphic or mero-morphic functio...
For a nonconstant holomorphic map between projective Riemann surfaces with conformal metrics, we con...
Abstract. It is well known that the Schwarzian derivative of an analytic map defined in a domain in ...
This thesis is a study of three topics, each of which describes an aspect of the geometry of conform...
Abstract. Minda and Peschl invented a kind of derivative of maps between Riemann surfaces, which dep...
Abstract. Combining the definition of Schwarzian derivative for conformal mappings be-tween Riemanni...
The boundary at infinity of a quasifuchsian hyperbolic manifold is equiped with a holomorphic quadra...
We observe that in contrast to the class S, the extremal functions for the bound of higher order Sch...
Abstract. We consider the Schwarzian derivative Sf of a complex polynomial f and its iterates. We sh...
Our first objective in this paper is to give a natural formulation of the Christof-fel problem for h...
Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and O...
This paper is a survey of some new techniques and new results on sufficient conditions in terms of t...
Let Ω and Π be two hyperbolic simply connected domains in the extended complex plane C̄ = C ∪ {∞}. W...
grantor: University of TorontoLet 'D' be the unit disc in the complex plane, and lz=1 1-...
Abstract. This paper shows how new dierential geometric ap-proaches to univalence criteria involving...
Abstract. Peschl defined invariant higher-order derivatives of a holomorphic or mero-morphic functio...
For a nonconstant holomorphic map between projective Riemann surfaces with conformal metrics, we con...
Abstract. It is well known that the Schwarzian derivative of an analytic map defined in a domain in ...
This thesis is a study of three topics, each of which describes an aspect of the geometry of conform...
Abstract. Minda and Peschl invented a kind of derivative of maps between Riemann surfaces, which dep...
Abstract. Combining the definition of Schwarzian derivative for conformal mappings be-tween Riemanni...
The boundary at infinity of a quasifuchsian hyperbolic manifold is equiped with a holomorphic quadra...
We observe that in contrast to the class S, the extremal functions for the bound of higher order Sch...
Abstract. We consider the Schwarzian derivative Sf of a complex polynomial f and its iterates. We sh...
Our first objective in this paper is to give a natural formulation of the Christof-fel problem for h...
Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and O...
This paper is a survey of some new techniques and new results on sufficient conditions in terms of t...
Let Ω and Π be two hyperbolic simply connected domains in the extended complex plane C̄ = C ∪ {∞}. W...