Conformal Maps and Geometry

  title={Conformal Maps and Geometry},
  author={Dmitry Beliaev},
  journal={Advanced Textbooks in Mathematics},
  • D. Beliaev
  • Published 13 November 2019
  • Mathematics
  • Advanced Textbooks in Mathematics
3 Citations
Complex Generalized Integral Means Spectrum of Drifted Whole-Plane SLE and LLE
We present new exact results for the complex generalized integral means spectrum (in the sense of [DHLZ18]) for two kinds of whole-plane Loewner evolutions driven by a Lévy process: (1) The case of a
Large deviations of multichordal SLE$_{0+}$, real rational functions, and zeta-regularized determinants of Laplacians
We prove a strong large deviation principle (LDP) for multiple chordal SLE$_{0+}$ curves with respect to the Hausdorff metric. In the single chordal case, this result strengthens an earlier partial
Topological characterisations of Loewner traces
The (chordal) Loewner differential equation encodes certain curves in the half-plane (aka traces) by continuous real-valued driving functions. Not all curves are traces; the latter can be defined via


Fixed points, Koebe uniformization and circle packings
A domain in the Riemann sphere \(\hat{\mathbb{C}}\) is called a circle domain if every connected component of its boundary is either a circle or a point. In 1908, P. Koebe [Ko1] posed the following
Real and complex analysis
Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures
Convergence of a Variant of the Zipper Algorithm for Conformal Mapping
Convergence for Jordan regions in the sense of uniformly close boundaries is proved and corresponding uniform estimates on the closed region and the closed disc for the mapping functions and their inverses are given.