Preprints

• Conformal Welding for Finitely Connected Domains , preprint, accepted for publication in Computional Methods and Function Theory.
  
  
• The Uniformization Theorem , preprint
  
  
• Lens chains and the geodesic algorithm for conformal mapping , preprint
  
  
• Angular Derivatives and Lipschitz Majorants.
  Much of this material is now incorporated into the book Harmonic Measure, with J. Garnett (see below).
  
  
  
  The geodesic algorithm can be found in Math 534 Notes, near the end. There is a more understandable proof of Jorgensen's theorem based on harmonic measure, but the students do not see harmonic measure until the second quarter of the class. See also Math 534 for other material.

Recent publications

• 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.