Harmonic measure of the outer boundary of colander sets

2019/11/30 by Glücksam, Adi
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.00247

Abstract

We present two companion results: Phragmén-Lindelöf type tight bounds on the minimal possible growth of subharmonic functions with recurrent zero set, and tight bounds on the maximal possible decay of the harmonic measure of the outer boundary of colander sets.

Related

• Phragmén-Lindelöf theorems and p-harmonic measures for sets near low-dimensional hyperplanes
• The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(⋅)-harmonic measures
• Self-improving estimates of growth of subharmonic and analytic functions
• Harmonic measure on sets of codimension larger than one
• Harmonic measure and "locally flat" domains