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Discs in complex manifolds with no bounded plurisubharmonic functions
Author(s):
Jean-Pierre
Rosay
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2315-2319.
MSC (2000):
Primary 32H02, 32U05, 32Q65
Posted:
February 19, 2004
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Abstract:
Roughly speaking: In a complex manifold on which all bounded plurisubharmonic functions are constant, the center of a holomorphic disc and its boundary can be prescribed somewhat arbitrarily.
References:
-
- 1.
- F. Lárusson and R. Sigurdsson, Plurisubharmonic functions and analytic discs on manifolds, J. Reine Angew. Math. 501 (1998), 1-39. MR 99e:32020
- 2.
- A. Edigarian, A note on J. P. Rosay's paper: ``Poletsky theory of disks on holomorphic manifolds'', Ann. Polon. Math. 80 (2003), 125-132.
- 3.
- E. Poletsky, Plurisubharmonic functions as solutions of variational problems, Proc. Sympos. Pure Math. 52 (1991), 163-171. MR 92h:32022
- 4.
- J.-P. Rosay, Poletsky theory of disks on holomorphic manifolds, Indiana Univ. Math. J. 52 (2003), 157-169. MR 2004a:32053
- 5.
- J.-P. Rosay, Approximation of non-holomorphic maps, and Poletsky theory of discs, J. Korean Math. Soc. 40 (2003), no. 3, 423-434. MR 2004c:32065
- 6.
- H. L. Royden, The extension of regular holomorphic maps, Proc. Amer. Math. Soc. 43 (1974), 306-310. MR 49:629
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Additional Information:
Jean-Pierre
Rosay
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email:
jrosay@math.wisc.edu
DOI:
10.1090/S0002-9939-04-07460-X
PII:
S 0002-9939(04)07460-X
Received by editor(s):
April 24, 2003
Posted:
February 19, 2004
Additional Notes:
Partly supported by NSF
Communicated by:
Mei-Chi Shaw
Copyright of article:
Copyright
2004,
American Mathematical Society
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