Topology of quadrature domains
نویسندگان
چکیده
منابع مشابه
Topology of Quadrature Domains
Formulas like (0.1) and (0.2) are called quadrature identities, and the corresponding domains of integration are called (classical) quadrature domains. Various classes of quadrature domains have been known for quite some time, see e.g. Neumann’s papers [39, 40] from the beginning of the last century, but the systematic study began only with the work of Davis [13], and Aharonov and Shapiro [2]. ...
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It is well known that, in the plane, the boundary of any quadrature domain (in the classical sense) coincides with the zero set of a polynomial. We show, by explicitly constructing some four-dimensional examples, that this is not always the case. This confirms, in dimension 4, a conjecture of the second author. Our method is based on the Schwarz potential and involves elliptic integrals of the ...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2015
ISSN: 0894-0347,1088-6834
DOI: 10.1090/jams828