scholarly journals Barycentric interpolation and mappings on smooth convex domains

2010 ◽  
Author(s):  
Michael S. Floater ◽  
Jiří Kosinka
Keyword(s):  
Smooth Convex ◽  
Convex Domains ◽  
Barycentric Interpolation

scholarly journals Zero varieties for the Nevanlinna class on all convex domains of finite type

2001 ◽  
Vol 163 ◽  
pp. 215-227 ◽  
Author(s):  
Klas Diederich ◽  
Emmanuel Mazzilli
Keyword(s):  
Finite Type ◽  
Convex Domain ◽  
Main Tool ◽  
Smooth Convex ◽  
Convex Domains ◽  
Zero Sets ◽  
Nevanlinna Class ◽  
Cauchy Riemann ◽  
Bounded Smooth

It is shown, that the so-called Blaschke condition characterizes in any bounded smooth convex domain of finite type exactly the divisors which are zero sets of functions of the Nevanlinna class on the domain. The main tool is a non-isotropic L1 estimate for solutions of the Cauchy-Riemann equations on such domains, which are obtained by estimating suitable kernels of Berndtsson-Andersson type.

scholarly journals Regularity of complex geodesics and (non-)Gromov hyperbolicity of convex tube domains

2018 ◽  
Vol 30 (1) ◽  
pp. 159-170
Author(s):  
Peter Pflug ◽  
Włodzimierz Zwonek
Keyword(s):  
Convex Domain ◽  
Gromov Hyperbolicity ◽  
Smooth Convex ◽  
Tube Domain ◽  
Convex Domains ◽  
Hilbert Metric ◽  
Kobayashi Distance ◽  
Continuity Properties ◽  
Gromov Hyperbolic ◽  
Tube Domains

Abstract We deliver examples of non-Gromov hyperbolic tube domains with convex bases (equipped with the Kobayashi distance). This is shown by providing a criterion on non-Gromov hyperbolicity of (non-smooth) domains. The results show the similarity of geometry of the bases of non-Gromov hyperbolic tube domains with the geometry of non-Gromov hyperbolic convex domains. A connection between the Hilbert metric of a convex domain Ω in {\mathbb{R}^{n}} with the Kobayashi distance of the tube domain over the domain Ω is also shown. Moreover, continuity properties up to the boundary of complex geodesics in tube domains with a smooth convex bounded base are also studied in detail.

scholarly journals q ‐pseudoconvex and q ‐holomorphically convex domains

2019 ◽  
Vol 292 (12) ◽  
pp. 2619-2623
Author(s):  
George‐Ionuţ Ioniţă ◽  
Ovidiu Preda
Keyword(s):  
Convex Domains
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