an:00233058
Zbl 0792.30005
Bishop, Christopher J.
Some questions concerning harmonic measure
EN
Dahlberg, B. (ed.) et al., Partial differential equations with minimal smoothness and applications. Proceedings of an IMA Participating Institutions (PI) conference, held Chicago, IL, USA, March 21-25, 1990. New York etc.: Springer-Verlag. IMA Vol. Math. Appl. 42, 89-97 (1992).
1992
a
30C35 30C55
twist points; eigenvalues of Laplacian; harmonic measure
This paper discusses a variety of open problems involving the metric properties of harmonic measure (for the Laplacian) on domains in the plane. Most of the problems deal with the relation between harmonic measure and Hausdorff measures and particularly with 1-dimensional measure. There is also a discussion of recent related work by Jones, Makarov, Wolff and the author, among others. The paper ends by discussing some problems involving the geometry of Brownian paths in the plane and the random growth model called diffusion limited aggregation.
For the entire collection see [Zbl 0762.00004].
Ch.J.Bishop