Yifei Pan

Note on Schwarz-Pick estimates for bounded and positive real part analytic functions

In this note we consider higher order derivatives of bounded analytic functions.

A hopf lemma for holomorphic functions and applications

A new boundary uniqueness result for holomorphic functions is obtained. Applications are provided.

A remark on unique continuation

In this paper a unique continuation result is proved for differential inequality of second order.

A Schwarz–Pick lemma for the modulus of holomorphic mappings

In this paper, we prove a Schwarz–Pick lemma for the modulus of holomorphic mappings between the unit balls in complex spaces. This extends the classical Schwarz–Pick lemma and the related result proved by Pavlovi.

Real analyticity of homeomorphic CR mappings between real analytic hypersurfaces in

In this note, we prove a real analyticity result for smooth CR homeomorphisms in C2 .

Smooth counterexamples to strong unique continuation for a Beltrami system in C 2

We construct an example of a smooth map ℂ → ℂ2 which vanishes to infinite order at the origin, and such that the ratio of the norm of the derivative to the norm of the z derivative also vanishes to infinite order. This gives a counterexample to strong unique continuation for a vector valued analogue of the Beltrami equation.

Berezin's operator calculus and higher order Schwarz–Pick lemma

We provide a new and simple proof to the result in our study of Berezins operator calculus [B. Li, The Berezin transform and mth order Bergman metric, Trans. Amer. Math. Soc. (to appear)] that the mth order Bergman metric (B m ∂ v )(z) is a constant multiple of {(B 1∂ v )(z)} m on the unit ball, where (B 1∂ v )(z) is the classical Bergman metric. Based on the reproducing-kernel theory, an approximation approach is developed to treat (B m ∂ v )(z) on the unit ball and ℂ n in a uniform way. Secondly, we discuss the interplay between our analysis in Berezins operator calculus and the higher order Schwarz–Pick lemma in Dai et al. [S. Dai, H. Chen, and Y. Pan, The Schwarz–Pick lemma of high order in several variables, Michigan Math. J. (to appear)]. As a consequence, the mth order Carathéodory–Reiffen metric (C m ∂ v )(z) is shown to be a constant multiple of {(C 1∂ v )(z)} m also on the unit ball, where (C 1∂ v )(z) is the classical infinitesimal Carathéodory–Reiffen metric.

On higher order angular derivatives – an application of Faà di Bruno's formula

We study the singular behaviour of k-th angular derivatives of analytic functions in the unit disk in the complex plane ℂ and positive harmonic functions in the unit ball in ℝ n . Faà di Brunos formula is a crucial tool in our proofs.

Proper holomorphic self-mappings of hartogs domains in

In this paper it is proved that every paper holomorphic self mapping of a certain Hartogs domain is biholomorphic.