Harmonic measure of the outer boundary of colander sets
Adi Gl\"ucksam
TL;DR
This paper establishes precise bounds on the growth of subharmonic functions with recurrent zero sets and on the decay of harmonic measure for the outer boundary of colander sets, advancing understanding in potential theory.
Contribution
It provides new tight bounds in potential theory for subharmonic functions and harmonic measure related to colander sets, a novel theoretical development.
Findings
Tight bounds on subharmonic function growth with recurrent zero sets
Tight bounds on harmonic measure decay of colander set boundaries
Advances in potential theory and boundary behavior analysis
Abstract
We present two companion results: Phragm\'en-Lindel\"of 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.
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