On support points of the class $S^0(B^n)$
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- by Sebastian Schleißinger PDF
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Abstract:
We consider support points of the class $S^0(B^n)$ introduced by G. Kohr and prove that, given a normalized Loewner chain $f(z,t)$ such that $f(\cdot ,0)$ is a support point of $S^0(B^n),$ all elements of the chain are support points of $S^0(B^n).$ Also, we prove a similar result for Loewner chains that come from the Roper–Suffridge extension operator.References
- Leandro Arosio, Filippo Bracci, and Erlend Fornaess Wold, Solving the Loewner PDE in complete hyperbolic starlike domains of $\mathbb {C}^N$, eprint arXiv:1207.2721.
- Erik Andersén and László Lempert, On the group of holomorphic automorphisms of $\textbf {C}^n$, Invent. Math. 110 (1992), no. 2, 371–388. MR 1185588, DOI 10.1007/BF01231337
- Ian Graham, Hidetaka Hamada, Gabriela Kohr, and Mirela Kohr, Extreme points, support points and the Loewner variation in several complex variables, Sci. China Math. 55 (2012), no. 7, 1353–1366. MR 2943779, DOI 10.1007/s11425-012-4376-0
- Ian Graham and Gabriela Kohr, Geometric function theory in one and higher dimensions, Monographs and Textbooks in Pure and Applied Mathematics, vol. 255, Marcel Dekker, Inc., New York, 2003. MR 2017933, DOI 10.1201/9780203911624
- Ian Graham, Gabriela Kohr, and John A. Pfaltzgraff, Parametric representation and linear functionals associated with extension operators for biholomorphic mappings, Rev. Roumaine Math. Pures Appl. 52 (2007), no. 1, 47–68. MR 2341607
- D. J. Hallenbeck and T. H. MacGregor, Linear problems and convexity techniques in geometric function theory, Monographs and Studies in Mathematics, vol. 22, Pitman (Advanced Publishing Program), Boston, MA, 1984. MR 768747
- Gabriela Kohr, Using the method of Löwner chains to introduce some subclasses of biholomorphic mappings in $\textbf {C}^n$, Rev. Roumaine Math. Pures Appl. 46 (2001), no. 6, 743–760 (2002). MR 1929522
- John Wermer, An example concerning polynomial convexity, Math. Ann. 139 (1959), 147–150 (1959). MR 121500, DOI 10.1007/BF01354873
Additional Information
- Sebastian Schleißinger
- Affiliation: Department of Mathematics, University of Wuerzburg, 97074 Wuerzburg, Germany
- MR Author ID: 971431
- Email: sebastian.schleissinger@mathematik.uni-wuerzburg.de
- Received by editor(s): August 21, 2012
- Received by editor(s) in revised form: November 26, 2012, and December 3, 2012
- Published electronically: July 16, 2014
- Communicated by: Franc Forstnerič
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 3881-3887
- MSC (2010): Primary 32H02
- DOI: https://doi.org/10.1090/S0002-9939-2014-12106-X
- MathSciNet review: 3251727