Page 1

Displaying 1 – 18 of 18

Showing per page

Carathéodory balls and norm balls in H p , n = z n : z p < 1

Binyamin Schwarz, Uri Srebro (1996)

Banach Center Publications

It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on H p , n = z n : z p < 1 which are balls with respect to the complex l p norm in n are those centered at the origin.

Carathéodory balls in convex complex ellipsoids

Włodzimierz Zwonek (1996)

Annales Polonici Mathematici

We consider the structure of Carathéodory balls in convex complex ellipsoids belonging to few domains for which explicit formulas for complex geodesics are known. We prove that in most cases the only Carathéodory balls which are simultaneously ellipsoids "similar" to the considered ellipsoid (even in some wider sense) are the ones with center at 0. Nevertheless, we get a surprising result that there are ellipsoids having Carathéodory balls with center not at 0 which are also ellipsoids.

Completeness of the inner kth Reiffen pseudometric

Paweł Zapałowski (2002)

Annales Polonici Mathematici

We give an example of a Zalcman-type domain in ℂ which is complete with respect to the integrated form of the (k+1)st Reiffen pseudometric, but not complete with respect to the kth one.

Complex geodesics of the minimal ball in n

Peter Pflug, El Hassan Youssfi (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this note we give a characterization of the complex geodesics of the minimal ball in n . This answers a question posed by Jarnicki and Pflug (cf. [JP], Example 8.3.10)

Concave domains with trivial biholomorphic invariants

Witold Jarnicki, Nikolai Nikolov (2002)

Annales Polonici Mathematici

It is proved that if F is a convex closed set in ℂⁿ, n ≥2, containing at most one (n-1)-dimensional complex hyperplane, then the Kobayashi metric and the Lempert function of ℂⁿ∖ F identically vanish.

Currently displaying 1 – 18 of 18

Page 1