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Topology of quadrature domains


Authors: Seung-Yeop Lee and Nikolai G. Makarov
Journal: J. Amer. Math. Soc. 29 (2016), 333-369
MSC (2010): Primary 30C99, 30E05, 30E99, 30D05, 31A99; Secondary 76D27, 30C62
DOI: https://doi.org/10.1090/jams828
Published electronically: May 11, 2015
MathSciNet review: 3454377
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Abstract: We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity.


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Additional Information

Seung-Yeop Lee
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: duxlee@caltech.edu

Nikolai G. Makarov
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: makarov@caltech.edu

DOI: https://doi.org/10.1090/jams828
Received by editor(s): July 15, 2013
Received by editor(s) in revised form: November 13, 2014
Published electronically: May 11, 2015
Additional Notes: The first author was supported by Sherman Fairchild Senior Research Fellowship.
The second author was supported by NSF grant no. 1101735.
Article copyright: © Copyright 2015 American Mathematical Society