zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Proper holomorphic maps from domains in 2 with transverse circle action. (English) Zbl 1143.32011

Let T=S 1 denote the torus and let Ω be a bounded connected open subset of 2 , which is pseudoconvex, of finite type and with smooth three dimensional boundary.

In this paper the authors consider proper holomorphic mappings between pseudoconvex regions of 2 and they study transverse actions in relation with the branch locus. Recall that classes of domains admitting a T-action are for instance Hartogs domains, Reinhardt and quasi-circular domains.

32H35Proper mappings, finiteness theorems
32T25Finite type domains
[1]Barrett, D., Regularity of the Bergman projection on domains with transverse symmetries, Math. Ann., 258(4), 1981/82, 441–446. MR0650948 (83i:32032) · Zbl 0486.32015 · doi:10.1007/BF01453977
[2]Coupet, B., Pan, Y. and Sukhov, A., On proper holomorphic mappings from domains with T-action, Nagoya Math. J., 154, 1999, 57–72. MR1689172 (2000b:32036)
[3]Pan, Y., Proper holomorphic self-mappings of Reinhardt domains, Math. Z., 208(2), 1991, 289–295. MR1128711 (93f:32029) · Zbl 0727.32011 · doi:10.1007/BF02571526
[4]Coupet B., Pan, Y., and Sukhov, A., Proper holomorphic self-maps of quasi-circular domains in 2, Nagoya Math. J., 164, 2001, 1–16. MR1869091 (2002j:32014)
[5]D’Angelo, J., Several Complex Variables and the Geometry of Real Hypersurfaces, CRC Press, Boca Raton, 1993. MR1224231 (94i:32022)
[6]Bedford, E., Action of the automorphisms of a smooth domain in n , Proc. Amer. Math. Soc., 93(2), 1985, 232–234. MR0770527 (86e:32029)
[7]Bell, S., Boundary behavior of proper holomorphic mappings between non-pseudoconvex domains, Amer. J. Math., 106(3), 1984, 639–643. MR0745144 (86a:32054) · Zbl 0552.32019 · doi:10.2307/2374288
[8]Bell, S. and Catlin, D., Boundary regularity of proper holomorphic mappings, Duke Math. J., 49, 1982, 385–396. MR0659947 (84b:32037a) · Zbl 0486.32014 · doi:10.1215/S0012-7094-82-04924-9
[9]Diederich, K. and Fornæss, J. E., Boundary regularity of proper holomorphic mappings, Invent. Math., 67(3), 1982, 363–384. MR0664111 (84b:32037b) · Zbl 0501.32010 · doi:10.1007/BF01398927
[10]Range, R. M., Holomorphic Functions and Integral Representations in Several Complex Variables, GTM 108, Springer, New York, 1986. MR0847923 (87i:32001)
[11]Rudin, W., Function Theory in the Unit Ball of n , GMW 241, Springer-Verlag, New York, 1980. MR0601594 (82i:32002)
[12]Bedford, E., Proper holomorphic mappings, Bull. Amer. Math. Soc. (N.S.), 10(2), 1984, 157–175. MR073 3691 (85b:32041) · Zbl 0534.32009 · doi:10.1090/S0273-0979-1984-15235-2
[13]Bell, S., Local boundary behavior of proper holomorphic mappings, Complex Analysis of Several Variables, Proc. Sympos. Pure Math., 41, A. M. S., Providence, 1984, 1–7. MR0740867 (85j:32043)
[14]Bedford, E. and Fornæss, J. E., A construction of peak functions on weakly pseudoconvex domains, Annals of Math., 107(3), 1978, 555–568. MR0492400 (58 #11520) · Zbl 0392.32004 · doi:10.2307/1971128
[15]Fornæss, J. E. and McNeal, J., A construction of peak functions on some finite type domains, Amer. J. Math., 116(3), 1994, 737–755. MR1277453 (95j:32023) · Zbl 0809.32005 · doi:10.2307/2374998
[16]Diederich, K. and Fornæss, J. E., Proper holomorphic images of strictly pseudoconvex domains, Math. Ann., 259(2), 1982, 279–286. MR0656667 (83g:32026) · Zbl 0486.32013 · doi:10.1007/BF01457314
[17]Grauert, H. and Remmert, R., Coherent Analytic Sheaves, GMW 265, Springer, Berlin, 1984. MR0755331 (86a:32001)
[18]Bedford, E., Proper holomorphic mappings from strongly pseudoconvex domains, Duke Math. J., 49(2), 1982, 477–484. MR0659949 (84b:32036) · Zbl 0498.32011 · doi:10.1215/S0012-7094-82-04926-2
[19]Huang, X. and Ji, S., Global holomorphic extension of a local map and a Riemann mapping theorem for algebraic domains, Math. Res. Lett., 5(1–2), 1998, 247–260. MR1617897 (99d:32013)
[20]Boothby, W., An Introduction to Differentiable Manifolds and Riemannian Geometry, Second Edition, Pure and Applied Math., 120, Academic Press, Boston, 1986. MR0861409 (87k:58001)
[21]Diederich, K. and Fornæss, J. E., Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions, Invent. Math., 39(2), 1977, 129–141. MR0437806 (55 #10728) · Zbl 0353.32025 · doi:10.1007/BF01390105
[22]Pinčuk, S. I., A boundary uniqueness theorem for holomorphic functions of several complex variables, Mat. Zametki, 15(2), 1974, 205–212; English transl., Math. Notes, 15(1–2), 116–120. MR0350065 (50 #2558)
[23]Baouendi, M. S., Rothschild, L. P. and Trèves, F., CR structures with group action and extendability of CR functions, Invent. Math., 82(2), 1985, 359–396. MR0809720 (87i:32028) · Zbl 0598.32019 · doi:10.1007/BF01388808
[24]Chirka, E. M., Introduction to the geometry of CR manifolds, Uspekhi Mat. Nauk, 46(1), 1991, 81–164, Trans. in Russian Math. Surveys, 46(1), 1991, 95–197. MR1109037 (92m:32012)
[25]Tanaka, N., On the pseudo-conformal geometry of hypersurfaces of the space of n complex variables, J. Math. Soc. Japan, 14, 1962. 397–429. MR0145555 (26 #3086) · Zbl 0113.06303 · doi:10.2969/jmsj/01440397
[26]Bell, S. and Catlin, D., Regularity of CR mappings, Math. Z., 199(3), 1988, 357–368. MR0961816 (89i:32028) · Zbl 0639.32011 · doi:10.1007/BF01159784