Collisions and Spirals of Loewner Traces (2009)
Lind, Joan, Marshall, Donald E., Rohde, Steffen
We analyze Loewner traces driven by functions asymptotic to K\sqrt{1-t}. We prove a stability result when K is not 4 and show that K=4 can lead to non locally connected hulls. As a consequence, we...
AREA, CAPACITY AND DIAMETER VERSIONS OF SCHWARZ’S LEMMA (2008)
Robert B. Burckel, Donald E. Marshall, David Minda, Pietro Poggi-corradini, J. Ransford
Abstract. The now canonical proof of Schwarz’s Lemma appeared in a 1907 paper of Carathéodory, who attributed it to Erhard Schmidt. Since then, Schwarz’s Lemma has acquired considerable fame,...
Convergence of a variant of the Zipper algorithm for conformal mapping (2008)
Donald E. Marshall, Steffen Rohde
In the early 1980’s an elementary algorithm for computing conformal maps was discovered by R. Kühnau and the first author. The algorithm is fast and accurate, but convergence was not known. Given...
Area, capacity and diameter versions of Schwarz's Lemma (2008)
Burckel, Robert B., Marshall, Donald E., Minda, David, Poggi-Corradini, Pietro, Ransford, Thomas J.
The now canonical proof of Schwarz's Lemma appeared in a 1907 paper of Carath\'eodory, who attributed it to Erhard Schmidt. Since then, Schwarz's Lemma has acquired considerable fame, with multiple...
/relax THE ANGULAR DISTRIBUTION OF MASS BY BERGMAN FUNCTIONS (2007)
Donald E. Marshall, Wayne Smith
Abstract. LetD = {z: |z | < 1} be the unit disk in the complex plane and denote by dA two-dimensional Lebesgue measure on D. For ε> 0 we define Σε = {z: | arg z | < ε}. We prove that for...
Traps For Reflected Brownian Motion (2007)
Zhen-qing Chen, Donald E. Marshall
Consider an open set D 2, and a closed ball B D. Let E denote the expectation of the hitting time of B for reflected Brownian motion in D starting from x D. We say that D is a trap domain if sup x E...
Convergence of the Zipper algorithm for conformal mapping (2006)
Marshall, Donald E., Rohde, Steffen
In the early 1980's an elementary algorithm for computing conformal maps was discovered by R. K\"uhnau and the first author. The algorithm is fast and accurate, but convergence was not known. Given...
On a theorem of Landau and Toeplitz (2006)
Burckel, Robert B., Marshall, Donald E., Poggi-Corradini, Pietro
The now canonical proof of Schwarz's Lemma appeared in a 1907 paper of Carath\'eodory, who attributed it to Erhard Schmidt. Since then, Schwarz's Lemma has acquired considerable fame, with multiple...
The angular distribution of mass by Bergman functions (1999)
Smith, Wayne, Marshall, Donald E.
Let D = {z: |z| < 1} be the unit disk in the complex plane and denote by dA two-dimensional Lebesgue measure on D. For e > 0 we define Se = {z: |arg z| < e}. We prove that for every e > 0 there...