Hostname: page-component-f554764f5-rj9fg Total loading time: 0 Render date: 2025-04-11T11:47:32.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytic discs in the polynomial hull of a disc fibration over the sphere

Published online by Cambridge University Press:  17 April 2009

Miran Černe
Miran Černe
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, 1 111 Ljubljana, Slovenia e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that for each point P in the interior of the polynomial hull of a disc fibration X over the unit sphere ∂n there exists an H∞ analytic disc with boundary in X and passing through p.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 403 - 406
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Alexander, H. and Wermer, J., ‘Polynomial bulls with convex fibers’, Math. Ann. 266 (1981), 243–257.Google Scholar
[2]Bedford, E., ‘Survey of pluri-potential theory’, in Several Complex Variables: Proceeding of the Mittag-Leffler Institute, 1987–1988, Mathematical Notes 38 (Princeton University Press, Princeton, N.J., 1993), pp. 48–97.Google Scholar
[3]Forstnerič, F. ‘Polynomial hulls of sets fibered over the circle’, Indiana Univ. Math. J. 37 (1988), 869–889.CrossRefGoogle Scholar
[4]Gamelin, T.W., Uniform algebras and Jensen measures, London Mathematical Society, Lecture Notes Series 32 (Cambridge University Press, Cambridge, 1978).Google Scholar
[5]Klimek, M., Pluripotential theory, London Mathematical Society Monographs, New Series 6 (Oxford University Press, 1991).CrossRefGoogle Scholar
[6]Poletsky, E.A., ‘Plurisubharmonic functions as solution of variational problems’ in Several complex variables and complex geometry (Santa Cruz, CA, 1989), Proc. Sympos. Pure Math., Part 1 52 (American Mathematical Society, 1991), pp. 163–171.CrossRefGoogle Scholar
[7]Poletsky, E.A., ‘Holomorphic currents’, Indiana Univ. Math. J. 42 (1993), 85–144.CrossRefGoogle Scholar
[8]Rudin, W., Real and complex analysis (McGraw-Hill, New York, 1987).Google Scholar
[9]Slodkowski, Z., ‘Polynomial hulls with convex fibers and complex geodesics’, J. Func. Anal. 94 (1990), 156–176.CrossRefGoogle Scholar
[10]Slodkowski, Z., ‘Polynomial hulls in ℂ2 and quasicircles’, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 16 (1989), 367–391.Google Scholar
[11]Whittlesey, M.A., ‘Polynomial hulls with disk fibers over the ball in ℂ2’, Michigan Math. J. 44 (1997), 475–494.CrossRefGoogle Scholar