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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The Loewner differential equation and slit mappings


Authors: Donald E. Marshall and Steffen Rohde
Journal: J. Amer. Math. Soc. 18 (2005), 763-778
MSC (2000): Primary 30C45, 30C20; Secondary 30C62, 30C30
Published electronically: June 10, 2005
MathSciNet review: 2163382
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the Loewner equation generates slits if the driving term is Hölder continuous with exponent 1/2 and small norm and that this is best possible.


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Additional Information

Donald E. Marshall
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
Email: marshall@math.washington.edu

Steffen Rohde
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
Email: rohde@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-05-00492-3
PII: S 0894-0347(05)00492-3
Keywords: Conformal maps, harmonic measure, quasiconformal maps, quasiarc, conformal welding, Loewner's differential equation, Lipschitz continuous, H\"older continuous
Received by editor(s): July 1, 2003
Published electronically: June 10, 2005
Additional Notes: The authors were partially supported by NSF grants DMS-9800464, DMS-9970398, and DMS-0201435.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.