Donald E. Marshall

Professor, appointed 1976 (Ph.D. UCLA 1976)

Research area: Complex analysis

Personal Web page: http://www.math.washington.edu/~marshall/personal.html
E-mail: marshall[_a_t_]math.washington.edu
Phone: 543-9352
Office: PDL C-555
Courses taught this quarter: 536A

Hobbies: Hiking, soccer, Scandinavian folk-dancing, auto repair, sailing

Professional interests

My research centers on problems about functions of one complex variable, usually involving geometric estimates of harmonic measure. Many times these problems arise in other areas of mathematical research such as functional analysis, numerical analysis and probability. Topics include bounded analytic functions, univalent functions, extremal length, harmonic measure and the numerical computation of conformal maps.

The recently completed book, Harmonic Measure, with J. Garnett, devotes the first four chapters to classical material suitable for a second year course (graduate) in complex analysis, while the last four chapters cover recent advances on Bloch functions, Brennan's conjecture, harmonic measure in infinitely connected domains, rectifiability and other topics in geometric function theory.

Selected bibliography

The Loewner Differential Equation and Slit Mappings, with S. Rohde, J. Amer. Math. Soc. 18 (2005), no. 4, 763-778.

"Harmonic Measure", with J. Garnett, Cambridge University Press, June 2005, 587pp.

A Lipschitz Decomposition of Minimal Surfaces, with J. Garnett and P. Jones, J. Diff. Geo. 35 (1992), 659-673.

Frequency Domain Design and Analytic Selections, with J. W. Helton, Indiana Univ. Math. J. 39 (1990), 157-184.

On a Sharp Inequality Concerning the Dirichlet Integral, with S.-Y.A. Chang, Amer. J. Math. 107 (1985), 1015-1033.

Critical Points of Green's Function, Harmonic Measure, and the Corona Problem, with P. Jones, Ark. för Mat. 23 (1985), 281-314.

Subalgebras of L^∞ containing H^∞, Acta Math. 137 (1976), 91-98.

Zipper, Fortran programs for numerical computation of conformal maps, and C programs for X-11 graphics display of the maps. Sample pictures, Fortran and C code available at URL: http://www.math.washington.edu/~marshall/zipper.html