Conformal Laminations

Citation

Gupta, Vineet (2004) Conformal Laminations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MQAY-KR87. https://resolver.caltech.edu/CaltechETD:etd-05132004-233348

Abstract

A lamination on a circle is an equivalence relation on the points of the circle. Laminations can be induced on a circle by a map that is continuous on the closed disc and injective in the interior. Such laminations are characterized topologically, as being flat and closed. In this paper we investigate the conditions under which a closed, flat lamination is induced by a conformal mapping. We show that if the set of multiple points of the lamination form a Cantor set, whose end points are identified under the lamination, then the lamination is conformal. More generally, the union of such laminations is also conformal. We also show conjecture that any closed, flat lamination, such that the set of multiple points is of logarithmic capacity zero, is conformal.

Thesis Files