|
Holomorphic families of long  's
Author:
Franc Forstnerič
Journal:
Proc. Amer. Math. Soc. 140 (2012), 2383-2389
MSC (2010):
Primary 32E10, 32E30, 32H02
Posted:
November 3, 2011
Full-text PDF
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We construct a holomorphically varying family of complex surfaces  , parametrized by the points  in any Stein manifold, such that every  is a long  which is biholomorphic to  for some but not all values of  .
References
- 1.
Erik
Andersén and László
Lempert, On the group of holomorphic automorphisms of
𝐶ⁿ, Invent. Math. 110 (1992),
no. 2, 371–388. MR 1185588
(93i:32038), http://dx.doi.org/10.1007/BF01231337
- 2.
John
Erik Fornaess, An increasing sequence of Stein manifolds whose
limit is not Stein, Math. Ann. 223 (1976),
no. 3, 275–277. MR 0417448
(54 #5498)
- 3.
John
Erik Fornæss, Short ℂ^{𝕜}, Complex
analysis in several variables—Memorial Conference of Kiyoshi
Oka’s Centennial Birthday, Adv. Stud. Pure Math., vol. 42,
Math. Soc. Japan, Tokyo, 2004, pp. 95–108. MR 2087041
(2005h:32027)
- 4.
Franc
Forstnerič and Jean-Pierre
Rosay, Approximation of biholomorphic mappings by automorphisms of
𝐶ⁿ, Invent. Math. 112 (1993),
no. 2, 323–349. MR 1213106
(94f:32032), http://dx.doi.org/10.1007/BF01232438
- 5.
Jean-Pierre
Rosay and Walter
Rudin, Holomorphic maps from
𝐶ⁿ to 𝐶ⁿ, Trans.
Amer. Math. Soc. 310 (1988), no. 1, 47–86. MR 929658
(89d:32058), http://dx.doi.org/10.1090/S0002-9947-1988-0929658-4
- 6.
Gabriel
Stolzenberg, The analytic part of the Runge hull, Math. Ann.
164 (1966), 286–290. MR 0203080
(34 #2938)
- 7.
Edgar
Lee Stout, The theory of uniform algebras, Bogden &
Quigley, Inc., Tarrytown-on-Hudson, N. Y., 1971. MR 0423083
(54 #11066)
- 8.
Dror
Varolin, The density property for complex manifolds and geometric
structures, J. Geom. Anal. 11 (2001), no. 1,
135–160. MR 1829353
(2002g:32026), http://dx.doi.org/10.1007/BF02921959
- 9.
Dror
Varolin, The density property for complex manifolds and geometric
structures. II, Internat. J. Math. 11 (2000),
no. 6, 837–847. MR 1785520
(2002g:32027), http://dx.doi.org/10.1142/S0129167X00000404
- 10.
John
Wermer, An example concerning polynomial convexity, Math. Ann.
139 (1959), 147–150 (1959). MR 0121500
(22 #12238)
- 11.
Erlend
Fornæss Wold, A Fatou-Bieberbach domain in ℂ²
which is not Runge, Math. Ann. 340 (2008),
no. 4, 775–780. MR 2372737
(2009c:32019), http://dx.doi.org/10.1007/s00208-007-0168-1
- 12.
Erlend
Fornæss Wold, A long ℂ² which is not Stein,
Ark. Mat. 48 (2010), no. 1, 207–210. MR 2594593
(2011c:32011), http://dx.doi.org/10.1007/s11512-008-0084-y
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (2010):
32E10,
32E30,
32H02
Retrieve articles in all journals
with MSC (2010):
32E10,
32E30,
32H02
Additional Information
Franc Forstnerič
Affiliation:
Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
Email:
franc.forstneric@fmf.uni-lj.si
DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-11092-X
PII:
S 0002-9939(2011)11092-X
Keywords:
Stein manifold,
Fatou-Bieberbach domain,
long $\mathbb{C}^{2}$
Received by editor(s):
January 18, 2011
Received by editor(s) in revised form:
February 17, 2011
Posted:
November 3, 2011
Additional Notes:
The author was supported by grants P1-0291 and J1-2152 from ARRS, Republic of Slovenia
Communicated by:
Mei-Chi Shaw
Article copyright:
© Copyright 2011 American Mathematical Society
|
