Bulletin of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-9485(e) ISSN 0273-0979(p)

Proper holomorphic mappings

Author(s): Eric Bedford
Journal: Bull. Amer. Math. Soc. 10 (1984), 157-175.
MSC (1980): Primary 32H99, 32E35; Secondary 32H10, 32F20, 32F15
MathSciNet review: 733691
Retrieve article in: PDF

References:

1.: L. Ahlfors, Open Riemann surfaces and extremal problems on compact subregions, Comment Math. Helv. 24 (1950), 100-132. MR 36318
2.: A. Aleksandrov, Math. Sb. 118 (160) (1982), 147-163. (Russian) MR 658785
3.: H. Alexander, Proper holomorphic mappings in C, Indiana Univ. Math. J. 26 (1977), 137-146. MR 422699
4.: H. Alexander, Explicit imbedding of the (punctured) disk into C², Comment Math. Helv. 52 (1977), 539-544. MR 481126
5.: D. Barrett, Regularity of the Bergman projection on domains with transverse symmetries, Math. Ann. 258 (1982), 441-446. MR 650948
6.: D. Barrett, Boundary analyticity of proper holomorphic maps of domains with non-analytic boundaries, Math. Ann. 263 (1983), 479-482. MR 707243
7.: D. Barrett, Holomorphic equivalence and proper mapping of bounded Reinhardt domains not containing the origin.
8.: D. Barrett, A smooth bounded domain in C
9.: E. Bedford, Holomorphic mapping of products of annuli in C, Pacific J. Math. 87 (1980), 27-281. MR 592735
10.: E. Bedford, Proper holomorphic mappings from strongly pseudoconvex domains, Duke Math. J. 49 (1982), 477-484. MR 659949
11.: E. Bedford, Proper holomorphic mappings from domains with real analytic boundary, Amer. J. Math. MR 745150
12.: E. Bedford and S. Bell, Proper self maps of weakly pseudoconvex domains, Math. Ann. 261 (1982), 47-49. MR 675205
13.: E. Bedford and S. Bell, Boundary continuity of proper holomorphic correspondences, Séminaire Dolbeault-Lelong-Skoda, 1983.
14.: E. Bedford and S. Bell, Proper correspondences of bounded domains in C, Proc. Colloque Analyse Complexe, Toulouse.
15.: E. Bedford and S. Bell, Boundary behavior of proper holomorphic correspondences.
16.: E. Bedford, S. Bell and D. Catlin, Boundary behavior of proper holomorphic mappings, Michigan Math. J. 30 (1983), 107-111. MR 694934
17.: E. Bedford and J. E. Fornaess, Biholomorphic maps of weakly pseudoconvex domains, Duke Math. J. 45 (1978), 711-719. MR 518102
18.: S. Bell, Biholomorphic mappings and the $\bar \partial $-problem, Ann. of Math. (2) 114 (1981), 103-113. MR 625347
19.: S. Bell, Proper holomorphic mappings and the Bergman projection, Duke Math. J. 48 (1981), 167-175. MR 610182
20.: S. Bell, Analytic hypoellipticity of the $\bar \partial $-Neumann problem and extendability of holomorphic mappings, Acta Math. 147 (1981), 109-116. MR 631091
21.: S. Bell, Proper holomorphic mappings between circular domains, Comment Math. Helv. 57 (1982), 532-538. MR 694605
22.: S. Bell, Boundary behavior of proper holomorphic mappings between non-pseudoconvex pseudoconvex domains, Amer. J. Math.
23.: S. Bell, Regularity of the Bergman projection in certain non-pseudoconvex domains, Pacific J. Math. 105 (1983), 273-278. MR 691602
24.: S. Bell, Local boundary behavior of proper holomorphic mappings, Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, R. I., 1984. (to appear). MR 740867
25.: S. Bell and H. Boas, Regularity of the Bergman projection in weakly pseudoconvex domains, Math. Ann. 257 (1981), 23-30. MR 630644
26.: S. Bell and D. Catlin, Boundary regularity of proper holomorphic mappings, Duke Math. J. 49 (1982), 385-396. MR 659947
27.: V. K. Beloshapka and A. G. Vitushkin, Estimates for the radius of convergence of power series defining mappings of analytic hypersurfaces, Izv. Akad. Nauk SSSR 45 (1981), 962-984. MR 637612
28.: E. Bishop, Mappings of partially analytic spaces, Amer. J. Math. 83 (1961), 209-242. MR 123732
29.: D. Burns and S. Shnider, Geometry of hypersurfaces and mapping theorems in C, Comment Math. Helv. 54 (1979), 199-217. MR 535055
30.: D. Burns, S. Shnider and R. O. Wells, Deformation of strongly pseudoconvex domains, Invent Math. 46 (1978), 237-253. MR 481119
31.: H. Cartan, Quotients of complex analytic spaces, Contribution to Function Theory, Oxford Univ. Press, Bombay, 1960. MR 139769
32.: D. Catlin, Boundary invariants of pseudoconvex domains (to appear). MR 769163
33.: J. Cima, S. Krantz and T. Suffridge, A reflection principle for proper holomorphic mappings of strongly pseudoconvex domains and applications.
34.: J. Cima and T. Suffridge, A reflection principle with applications to proper holomorphic mappings, Math. Ann. MR 721883
35.: K. Diederich and J. E. Fornaess, Pseudoconvex domains: Bounded strictly plurisubharmonic exhaustion functions, Invent Math. 39 (1977), 129-147. MR 437806
36.: K. Diederich and J. E. Fornaess, Pseudoconvex domains with real-analytic boundary, Ann. of Math. (2) 107 (1978), 371-384. MR 477153
37.: K. Diederich and J. E. Fornaess, Biholomorphic mappings between certain real analytic domains in C, Math. Ann. 245 (1979), 255-272. MR 553344
38.: K. Diederich and J. E. Fornaess, Proper holomorphic images of strictly pseudoconvex domains, Math. Ann. 259 (1982), 279-286. MR 656667
39.: K. Diederich and J. E. Fornaess, Boundary regularity of proper holomorphic mappings, Invent Math. 67 (1982), 363-384. MR 664111
40.: K. Diederich and J. E. Fornaess, Proper holomorphic maps onto pseudoconvex domains with real-analytic boundary, Ann. of Math. (2) 110 (1979), 575-592. MR 554386
41.: K. Diederich and J. E. Fornaess, A remark on a paper of S. R. Bell, Manuscripta Math. 34 (1981), 31-44. MR 614388
42.: K. Diederich and I. Lieb., Konvexität in der komplexen Analysis, Birkhäuser, 1981. MR 698605
43.: K. Diederich and S. Webster, A reflection principle for degenerate real hypersurfaces, Duke Math. J. 47 (1980), 835-843. MR 596117
44.: J. Faran, Maps from the two-ball to the three-ball, Invent. Math. 68 (1982), 441-475. MR 669425
45.: J. Faran, The linearity of proper holomorphic maps between balls in the low codimension case.
46.: J. Faran, The non-imbeddability of real hypersurfaces in spheres (to appear).
47.: J. E. Fornaess, Embedding strictly pseudoconvex domains in convex domains, Amer. J. Math. 98 (1976), 529-569. MR 422683
48.: J. E. Fornaess, Bilohomorphic mappings between weakly pseudoconvex domains, Pacific J. Math. 74 (1978), 63-65. MR 481111
49.: O. Forster, Plongements des variétés de Stein, Comment Math. Helv 45 (1970), 170-184. MR 269880
50.: B. L. Fridman, On a class of analytic polyhedra, Dokl. Akad. Nauk SSSR 242 (1978) = Soviet Math. Dokl. 19 (1979), 1258-1961. MR 510253
51.: B. L. Fridman, On the imbedding of a strictly pseudoconvex domains in a polyhedron, Dokl. Akad. Nauk USSR 249 (1979) = Soviet Math. Dokl. 20 (1979), 1228-1232. MR 553986
52.: B. L. Fridman, One example of the boundary behaviour of biholomorphic transformations, Proc. Amer. Math. Soc. 89 (1983), 226-228. MR 712627
53.: R. Greene and S. Krantz, Deformation of complex structures, estimates for the $\bar \partial $-equation, and stability of the Bergman kernel, Adv. in Math. 43 (1982), 1-86. MR 644667
54.: M. Gromov and Ja. Èliašberg, Nonsingular mappings of Stein manifolds, Functional Anal. Appl. 5 (1971), 156-157. MR 301236
55.: H. Grunsky, Lectures on theory of functions in multiply connected domains, Vandenhoeck & Ruprecht, Göttingen, 1978. MR 463413
56.: M. Hakim and N. Sibony, Fonctions holomorphes bornées sur la boule unité de C, Invent Math. 67 (1982), 213-222. MR 665153
57.: G. Henkin, An analytic polyhedron is not holomorphically equivalent to a strictly pseudoconvex domains, Dokl. Akad. Nauk SSSR 210 (1973), 1026-1029 = Soviet Math. Dokl. 14 (1973), 858-862. MR 328125
58.: A. Huckleberry and E. Ormsby, Nonexistence of proper holomorphic maps between certain complex manifolds, Manuscripta Math. 26 (1978/79), 371-379. MR 520107
59.: J. Kohn, Subellipticity of the $\bar \partial $-Neumann problem on pseudoconvex domains: sufficient conditions, Acta Math. 142 (1979), 79-122. MR 512213
60.: J. Kohn, Boundary regularity of $\bar \partial $, Recent Developments in Several Complex Variables (J. E. Fornaess, ed.), Princeton Univ. Press, Princeton, N. J., 1981. MR 627746
61.: M. Landucci, Proper equivalence for a class of pseudoconvex domains, Trans. Amer. Math. Soc. (to appear). MR 732122
62.: H. Laufer, Imbedding annuli in C², J. Analyse Math. 26 (1973), 187-215. MR 346189
63.: L. Lempert, Imbedding strictly pseudoconvex domains into a ball, Amer. J. Math. 104 (1982), 901-904. MR 667541
64.: T. C. Li, Proper holomorphic mappings over bounded domains in C, Bull. Inst. Math. Acad. Sinica 6 (1978), 175-180. MR 492404
65.: T. C. Li, Proper self-mappings of the Hartogs triangle, Chinese J. Math. 6 (1978), 191-195. MR 529973
66.: E. Ligocka, On proper holomorphic and biholomorphic mappings between product domains, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 319-323. MR 628046
67.: E. Løw, A construction of inner functions on the unit ball in C, Invent Math. 67 (1982), 223-229. MR 665154
68.: R. Narasimhan, Imbedding of holomorphically complete complex spaces, Amer. J. Math. 82 (1960), 917-934. MR 148942
69.: R. Narasimhan, Several complex variables, Univ. of Chicago Press, Chicago, 1971. MR 342725
70.: S. Pinčuk, On proper holomorphic mappings of strictly pseudoconvex domains, Siberian Math. J. 15 (1974), 909-917. MR 355109
71.: S. Pinčuk, On the analytic continuation of holomorphic mappings, Mat. Sb. 98 (140) (1975), 416-435 = Math. USSR-Sb. 27 (1975). MR 393562
72.: S. Pinčuk, On holomorphic mappings of real analytic hypersurfaces, Mat. Sb. 105 (147) (1978) = Math. USSR-Sb. 34 (1978), 503-519. MR 496595
73.: S. Pinčuk, Proper holomorphic mappings of strictly pseudoconvex domains, Soviet Math. Dokl. 19 (1978), 804-807. MR 510886
74.: S. Pinčuk, Holomorphic inequivalence of some classes of domains in C, Math. USSR-Sb. 39 (1981) = Mat. Sb. 111 (153) (1980), 61-86. MR 560464
75.: E. Poleckii, The Euler-Lagrange equations for extremal holomorphic mappings of the unit disk.
76.: M. Range, The Carathéodory metric and holomorphic maps on a class of weakly pseudoconvex domains, Pacific J. Math. 78 (1978), 173-189. MR 513293
77.: R. Remmert, Sur les espaces analytiques holomorphement separables et holomorphement convexes, C. R. Acad. Sci. Paris 243 (1956), 118-121. MR 79808
78.: R. Remmert and K. Stein, Eigentliche holomorphe Abbildungen, Math. Z. 73 (1960), 159-189. MR 124528
79.: H. Rischel, Ein Satz über eigentliche holomorphe Abbildungen von analytischen Polyedergebieten, Math. Scand. 14 (1964), 220-224. MR 173023
80.: H. Rischel, Holomorphe Überlagerungskorrespondenzen, Math. Scand. 15 (1964), 49-63. MR 178160
81.: W. Rudin, Function theory on the unit ball of C, Springer-Verlag, 1980. MR 601594
82.: W. Rudin, Holomorphic maps that extend to automorphisms of a ball, Proc. Amer. Math. Soc. 81 (1981), 429-432. MR 597656
83.: W. Rudin, Proper holomorphic maps and finite reflection groups, Indiana Univ. Math. J. 31 (1982), 701-720. MR 667790
84.: A. Sadullaev, Inner functions in C, Math. Notes 19 (1976), 37-38.
85.: S. E. Šaronov, On holomorphic mappings of polyhedra, Mat. Sb. 116 (158) (1981) = Math. USSR-Sb. 44 (1983), 117-123. MR 632493
86.: G. Schüller, Beiträge zur Theorie der randeigentlichen Korrespondenzen, Dissertation, Univ. Duisberg, 1980.
87.: R. R. Simha, Über die kritischen Werte gewisser holomorpher Abbildungen, Manuscripta Math. 3 (1970), 97-104. MR 264115
88.: K. Stein, Maximale holomorphe und meromorphe Abbildungen. II, Amer. J. Math. 86 (1964), 823-868. MR 171030
89.: K. Stein, Topics on holomorphic correspondences, Rocky Mountain J. Math. 2 (1972), 443-463. MR 311945
90.: A. Vitushkin, Holomorphic extension of mappings of compact hypersurfaces, Math. USSR-Izv. 20 (1983), 27-33 = Izv. Akad. Nauk SSSR 46 (1982). MR 643891
91.: S. Webster, On the mapping problem for algebraic real hypersurfaces, Invent Math. 43 (1977), 53-68. MR 463482
92.: S. Webster, On mapping an n-ball into an (n + 1)-ball in complex space, Pacific J. Math. 81 (1979), 267-272. MR 543749
93.: S. Webster, Holomorphic mappings of domains with generic corners, Proc. Amer. Math. Soc. 86 (1982), 236-240. MR 667281
94.: B. Wong, A maximum principle on Clifford torus and nonexistence of proper holomorphic map from the ball to polydisk, Pacific J. Math. 87 (1980), 211-222. MR 590878
95.: J. P. D'Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. (2) 115 (1982), 615-637. MR 657241
96.: G. Henkin and E. Chirka, Boundary properties of holomorphic functions of several complex variables, J. Soviet Math. 5 (1976), 612-687.
97.: S. Pincuk, On the boundary behavior of analytic sets and algebroid mappings, Dokl. Akad. Nauk USSR 268 (1983), 296-298. (Russian) MR 688243

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|