|
On injectivity of quasiregular mappings
Author(s):
Tadeusz
Iwaniec;
Leonid
V.
Kovalev;
Jani
Onninen
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1783-1791.
MSC (2000):
Primary 30C62;
Secondary 37C10, 30D20
Posted:
December 23, 2008
MathSciNet review:
2470838
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We give sufficient conditions for a planar quasiregular mapping to be injective in terms of the range of the differential matrix.
References:
-
- 1.
- G. Alessandrini and R. Magnanini, The index of isolated critical points and solutions of elliptic equations in the plane, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 19 (1992), no. 4, 567-589. MR 1205884 (94c:35063)
- 2.
- J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. of Math. (2) 17 (1915), no. 1, 12-22. MR 1503516
- 3.
- K. Astala, Area distortion of quasiconformal mappings, Acta Math. 173 (1994), no. 1, 37-60. MR 1294669 (95m:30028b)
- 4.
- K. Astala, T. Iwaniec, and G. J. Martin, Elliptic partial differential equations and quasiconformal mappings in the plane, Princeton University Press, to appear.
- 5.
- I. Bendixson, Sur les courbes définies par des équations différentielles, Acta Math. 24 (1901), 1-88. MR 1554923
- 6.
- L.E.J. Brouwer, On continuous vector distributions on surfaces. II, Verhand. K. Ned. Akad. Wet. Afd. Nat. I. Reeks 12 (1910), 716-734. Available from http://www.digitallibrary.nl/proceedings/.
- 7.
- P. Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038 (30:1270)
- 8.
- B. Kirchheim, S. Müller, and V. Šverák, Studying nonlinear pde by geometry in matrix space, in ``Geometric analysis and nonlinear partial differential equations'', 347-395, Springer, Berlin, 2003. MR 2008346 (2006f:35087)
- 9.
- O. Lehto and K. I. Virtanen, Quasiconformal mappings in the plane, 2nd edition, Springer-Verlag, New York-Heidelberg, 1973. MR 0344463 (49:9202)
- 10.
- O. Martio and J. Väisälä, Elliptic equations and maps of bounded length distortion, Math. Ann. 282 (1988), no. 3, 423-443. MR 967022 (89m:35062)
- 11.
- R. Miniowitz, Normal families of quasimeromorphic mappings, Proc. Amer. Math. Soc. 84 (1982), no. 1, 35-43. MR 633273 (83c:30026)
- 12.
- S. Rickman, Quasiregular mappings, Springer-Verlag, Berlin, 1993. MR 1238941 (95g:30026)
- 13.
- R. T. Rockafellar, Convex analysis, Princeton University Press, Princeton, NJ, 1997. MR 1451876 (97m:49001)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
30C62,
37C10, 30D20
Retrieve articles in all Journals with
MSC (2000):
30C62,
37C10, 30D20
Additional Information:
Tadeusz
Iwaniec
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email:
tiwaniec@syr.edu
Leonid
V.
Kovalev
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email:
lvkovale@syr.edu
Jani
Onninen
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email:
jkonnine@syr.edu
DOI:
10.1090/S0002-9939-08-09820-1
PII:
S 0002-9939(08)09820-1
Keywords:
Quasiregular mapping,
injectivity,
differential inclusion
Received by editor(s):
July 21, 2008
Posted:
December 23, 2008
Additional Notes:
The first author was supported by the NSF grant DMS-0800416.
The second author was supported by the NSF grant DMS-0700549.
The third author was supported by the NSF grant DMS-0701059.
Communicated by:
Mario Bonk
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
