Über die Verteilung von gewissen Punktsystemen mit Extremaleigenschaften.
Uniformly perfect sets, Green's function, and fundamental domains.
Univalent functions of given transfinite diameter: A maximum modulus problem.
Univalent functions with range restrictions.
Unrectifiable 1-sets have vanishing analytic capacity.
We complete the proof of a conjecture of Vitushkin that says that if E is a compact set in the complex plane with finite 1-dimensional Hausdorff measure, then E has vanishing analytic capacity (i.e., all bounded anlytic functions on the complement of E are constant) if and only if E is purely unrectifiable (i.e., the intersection of E with any curve of finite length has zero 1-dimensional Hausdorff measure). As in a previous paper with P. Mattila, the proof relies on a rectifiability criterion using...
Use of logarithmic sums to estimate polynomials.