Preprints

• Derivation of Chordal Loewner from Radial Loewner, preprint, 2011.
  
  
• Lens chains and the geodesic algorithm for conformal mapping , preprint 2008
  The geodesic algorithm, with proof of convergence, can also be found in Complex Analysis, Cambridge Univ. Press, see below.
  
  
• The Uniformization Theorem, preprint, 2011 (rewrite of earlier version)
  This material has been incorporated into the book Complex Analysis, Camb. Univ. Press, 2019 (see below).
  Complex Analysis, by T.W. Gamelin, Springer, 2001, uses our earlier version.
  
  
• Angular Derivatives and Lipschitz Majorants, preprint, 1995.
  Much of this material is now incorporated into the book Harmonic Measure, with J. Garnett (see below).
  
  
• Instructions for accessing a catalog of Shabat polynomials up through degree 14
  
  

Recent publications

• Complex Analysis Cambridge University Press, 2019, ISBN: 9781107134829.
  Improvements and Errata
  
  See listings in:
  4 Best New Mathematical Analysis eBooks To Read in 2020
  100 Best Mathematical Analysis Books of All Time See #18 (as of 10/2021); #14 (as of 4/2022).
  
  Here is an Amazon page for the book.
  
  
• Obliquely Reflected Brownian Motion in Non-Smooth Planar Domains, with K. Burdzy, Z-Q. Chen, and K. Ramanan, Ann. Probab. 45 (2017), no. 5, 2971–3037.
  
  
• Conformal Welding for Finitely Connected Regions , Comput. Methods Funct. Theory 11 (2011), No. 2, 655--669.
  
  
• Collisions and Spirals of Loewner traces, with J. Lind and S. Rohde, Duke Math. J. 154 (2010), 527-573.
  
  
• Area, Capacity, and Diameter versions of Schwarz's Lemma with R. Burckel, D. Minda, P. Poggi-Corradini, and T. Ransford, Conform. Geom. Dyn. 12 (2008), 133-152.
  
  
• Convergence of a variant of the Zipper algorithm for conformal mapping, with S. Rohde, SIAM J. Numer. Anal. 45(2007), 2577-2609.
  
  
• Traps for Reflected Brownian Motion, with K. Burdzy and Z-Q. Chen, Math. Zeit. 252(2006), 103-132.
  
  
• The Loewner differential equation and slit mappings, with S. Rohde, Jour. Amer. Math. Soc., 18(2005), 763-778.
  
  
• Harmonic Measure with J. Garnett, Cambridge University Press, 2005, 587 pp.
         Table of Contents,  Typos, corrections, etc.