Über das Schwarzsche Lemma bei analytischen Funktionen von zwei komplexen Veränderlichen

  title={{\"U}ber das Schwarzsche Lemma bei analytischen Funktionen von zwei komplexen Ver{\"a}nderlichen},
  author={C. Carath{\'e}odory},
  journal={Mathematische Annalen},
Schwarz‐type lemmas for generalized holomorphic maps between pseudo‐Hermitian manifolds and Hermitian manifolds
In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds and Hermitian manifolds. By Bochner formulas and comparison theorems, we establish related Schwarz typeExpand
The Kobayashi distance in holomorphic dynamics and operator theory
These are the notes of a short course I gave in the school "Aspects m\'etriques et dynamiques en analyse complete", Lille, May 2015. The aim of this notes is to describe how to use a geometricExpand
Notes on Hilbert's 16th: experiencing Viro's theory
This text is intended to become in the long run Chapter 3 of our long saga dedicated to Riemann, Ahlfors and Rohlin. Yet, as its contents evolved as mostly independent (due to our inaptitude toExpand
Ahlfors circle maps and total reality: from Riemann to Rohlin
This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting theExpand
Holomorphe Abbildungen In Hyperbolische Räume
Es sei K die Kategorie aller reduzierten komplexen Raume (vergl. [7]) und Hol (X, Y) die Menge aller holomorphen Abbildungen eines komplexen Raumes X in einen komplexen Raum Y. Ist T einExpand
Inequalities for The Caratheodory and Poincare Metrics in Open Unit Balls
We generalize a known inequality relating the Euclidean and hyperbolic metrics in Poincaré’s unit ball model of hyperbolic space. Our generalization applies to Schwarz-Pick metrics in the open unitExpand
Les Invariants DiffÉRentiels dans La ThÉOrie des Fonctions de Plusieurs Variables Complexes
Dans la theorie classique des fonctions analytiques les invariants differentials furent intoduits pour la premiere fois par H.A.Schwarz en resolvant le probleme de representer conforme-ment soit unExpand
Complete Einstein-Kähler Metric and Holomorphic Sectional Curvature on $Y_{II}(r,p;K)$
The explicit complete Einstein-K\"{a}hler metric on the second type Cartan-Hartogs domain $Y_{II}(r,p;K)$ is obtained in this paper when the parameter $K$ equals $\frac p2+\frac 1{p+1}$. The estimateExpand
We discuss the Carathéodory and Kobayashi pseudometrics and their infinitesimal forms on complex Banach manifolds. Our discussiion includes a very elementary treatment of the Kobayashi pseudometricExpand
Operator and function theory of the symmetrized polydisc
We establish necessary conditions, in the form of the positivity of Pick-matrices, for the existence of a solution to the spectral Nevanlinna-Pick problem: Let k and n be natural numbers. Choose nExpand