Memoirs of the American Mathematical Society 2010; 269 pp; softcover Volume: 206 ISBN10: 0821848100 ISBN13: 9780821848104 List Price: US$93 Individual Members: US$55.80 Institutional Members: US$74.40 Order Code: MEMO/206/969
 For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the HeleShaw flow with a freeboundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow. Table of Contents  Introduction and main results
 Quadrature domains
 Construction of measures for localization
 Generalizations of the reflection theorem
 Continuous reflection property and smooth boundary points
 Proofs of (1) and (3) in Theorem 1.1
 Corners with right angles
 Properly open cusps
 Microlocalization and the localreflection theorem
 Modifications of measures in \(R^+\)
 Modifications of measures in \(R^\)
 Sufficient conditions for a cusp to be a laminarflow point
 Turbulentflow points
 The set of stationary points
 Open questions
 Bibliography
 Symbol index
 Index
