Using results of L. Lempert, we are able to construct parabolic exhaustions for strictly convex domains D⊂ℂm with center at any given point of D. Using the theory of parabolic spaces and the geometric properties of these exhaustions, we can characterize the strictly convex domains biholomorphic to a circular domain and in particular to the ball in ℂm.
Parabolic Exhaustions for Strictly Convex Domains / G. PATRIZIO. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - STAMPA. - 47:(1984), pp. 271-309. [10.1007/BF01174598]
Parabolic Exhaustions for Strictly Convex Domains
PATRIZIO, GIORGIO
1984
Abstract
Using results of L. Lempert, we are able to construct parabolic exhaustions for strictly convex domains D⊂ℂm with center at any given point of D. Using the theory of parabolic spaces and the geometric properties of these exhaustions, we can characterize the strictly convex domains biholomorphic to a circular domain and in particular to the ball in ℂm.
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