Math 581CA/582CA
Harmonic Measure
Don Marshall
Autumn 2004/Winter 2005, Monday/Wednesday/Friday 10:30
This course will be based on the book Harmonic Measure (see
http://www.math.washington.edu/~marshall/harmmeas.pdf
for the table of
contents). The first quarter will cover standard background material that
every student of function theory should know (Chapters I-IV, Appendices A,
D, F) which includes potential theory in the plane, extremal length,
conjugate functions, Hardy spaces, and Hausdorff measure. The second
quarter will cover more recent results such as Bloch functions and the
relation between harmonic and Hausdorff measures, the integrability of
conformal maps, angular derivatives and boundary conformality, Jones square
sum characterization of subsets of rectifiable curves, and other topics as
time allows.
Prerequisites:
This course will be accessible to students who have
completed 524/525/526 and 534/535/536.