MATH Seminar

Title: Harmonic measure, reduced extremal length and quasicircles
Defense: Dissertation
Speaker: Huiqiang Shi of Emory University
Contact: Huiqiang Shi, huiqiang.shi@emory.edu
Date: 2016-08-10 at 12:00PM
Venue: W302
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Abstract: This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In chapter 2, we mainly study two important conformal invariants: the extremal distance and the reduced extremal distance. Gives the estimate of extremal distance in the unit disk and the comparison of these two conformal invariants. In chapter 3 and 4, we give several necessary and sufficient conditions for the sewing homeomorphism of a Jordan domain to be bi-Lipschitz or bi-Holder, by using harmonic measure, extremal distance and reduced extremal distance. Furthermore, in chapter 5, we obtain some equivalent conditions for a Jordan curve to be a quasicircle. In chapter 6, we use the Robin capacity to define a new index and use this new index to characterize unit circle.