- 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
Angular Derivatives and Lipschitz Majorants, preprint,
Much of this material is now incorporated into the book Harmonic Measure,
with J. Garnett (see below).
for accessing a catalog of Shabat polynomials up
through degree 14
Complex Analysis Cambridge University Press, 2019, ISBN:
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.
with J. Garnett, Cambridge University Press,
2005, 587 pp.
Table of Contents, Typos, corrections, etc.
- A few of my publications:
- Math Reviews of my publications:
- Harmonic Measure
by C. Bishop, Bull. Amer. Math. Soc. 44 (2007), 267-276.
begins with a well-written introduction to the subject.
The material in these publications and preprints is based upon work
supported by the National Science Foundation, most recently under
Grant No. DMS-0900814.
Any opinions, findings, and conclusions or recommendations expressed
in this material are those of the author(s) and do not
necessarily reflect the views of the National Science Foundation.
Questions? Send them to me at:
Return to Don Marshall's home page.