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ABOUT THE BOOK

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences.

Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves.

This volume is dedicated to the memory of Alexander Vasiliev.

TABLE OF CONTENTS

1. On Polynomially Integrable Domains in Euclidean Spaces

   • Mark Agranovsky

   Pages 1-21

2. A Survey on the Maximal Number of Solutions of Equations Related to Gravitational Lensing

   • Catherine Bénéteau, Nicole Hudson

   Pages 23-38

3. Boundary Interpolation by Finite Blaschke Products

   • Vladimir Bolotnikov

   Pages 39-65

4. Support Points and the Bieberbach Conjecture in Higher Dimension

   • Filippo Bracci, Oliver Roth

   Pages 67-79

5. Some Unsolved Problems About Condenser Capacities on the Plane

   • Vladimir N. Dubinin

   Pages 81-92

6. Filtration of Semi-complete Vector Fields Revisited

   • Mark Elin, David Shoikhet, Toshiyuki Sugawa

   Pages 93-102

7. Polynomial Lemniscates and Their Fingerprints: From Geometry to Topology

   • Anastasia Frolova, Dmitry Khavinson, Alexander Vasil’ev

   Pages 103-128

8. Regularity of Mappings with Integrally Restricted Moduli

   • Anatoly Golberg, Ruslan Salimov

   Pages 129-140

9. Extremal Problems for Mappings with g-Parametric Representation on the Unit Polydisc in ℂⁿ

   • Ian Graham, Hidetaka Hamada, Gabriela Kohr

   Pages 141-167

10. Evolution of States of a Continuum Jump Model with Attraction

    • Yuri Kozitsky

    Pages 169-189

11. Problems on Weighted and Unweighted Composition Operators

    • Valentin Matache

    Pages 191-217

12. Harmonic Measures of Slit Sides, Conformal Welding and Extremum Problems

    • Dmitri Prokhorov

    Pages 219-230

13. Comparison Moduli Spaces of Riemann Surfaces

    • Eric Schippers, Wolfgang Staubach

    Pages 231-271

14. Asymptotic Ratio of Harmonic Measures of Sides of a Boundary Slit

    • Alexander Solynin

    Pages 273-299

15. Coupling of Gaussian Free Field with General Slit SLE

    • Alexey Tochin, Alexander Vasil’ev

    Pages 301-366

16. A Marx-Strohhacker Type Result for Close-to-Convex Functions

    • Nikola Tuneski, Mamoru Nunokawa, Biljana Jolevska-Tuneska

    Pages 367-372