# Small Modifications of Quadrature Domains

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*Makoto Sakai*

#### Table of Contents

# Table of Contents

## Small Modifications of Quadrature Domains

- Chapter 1. Introduction and Main Results 18 free
- Chapter 2. Quadrature Domains 916 free
- Chapter 3. Construction of Measures for Localization 2128
- Chapter 4. Generalizations of the Reflection Theorem 2532
- Chapter 5. Continuous Reflection Property and Smooth Boundary Points 3138
- Chapter 6. Proofs of (1) and (3) in Theorem 1.1 3744
- Chapter 7. Corners with Right Angles 4956
- Chapter 8. Properly Open Cusps 8592
- Chapter 9. Microlocalization and the Local-Reflection Theorem 95102
- Chapter 10. Modifications of Measures in R+ 129136
- Chapter 11. Modifications of Measures in R- 181188
- Chapter 12. Sufficient Conditions for a Cusp to be a Laminar-Flow Point 213220
- Chapter 13. Turbulent-Flow Points 251258
- Chapter 14. The Set of Stationary Points 261268
- Chapter 15. Open Questions 263270
- Bibliography 265272
- Symbol Index 267274
- Index 269276 free