Attraction of analytic disks and Hölder continuity of proper holomorphic maps. (Attraction des disques analytiques et continuité höldérienne d’applications holomorphes propres.) (French) Zbl 0831.32012

Jakóbczak, Piotr (ed.) et al., Topics in complex analysis. Proceedings of the semester on complex analysis, held in autumn of 1992 at the International Banach Center in Warsaw, Poland. Warszawa: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 31, 91-98 (1995).
The author is dealing with the Hölder continuity of a proper holomorphic map \(f : D_1 \to D_2\), \(D_1, D_2\) bounded domains in \(\mathbb{C}^n\), \(n \geq 2\). Using the notion of attraction of analytic discs he proves some new results for domains with piecewise smooth boundary. In particular he obtains the following generalization of a theorem of Range: If \(bD_1\) is piecewise smooth strictly pseudoconvex and satisfies the cone property of order \(\gamma\) then \(f\) extends to a map \(f : \overline D_1 \to \overline D_2\) Hölder continuous of exponent \(\gamma/2\).
For the entire collection see [Zbl 0816.00022].
Reviewer: G.Tomassini (Pisa)


32H40 Boundary regularity of mappings in several complex variables
32H35 Proper holomorphic mappings, finiteness theorems