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Conformal Laminations


Gupta, Vineet (2004) Conformal Laminations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MQAY-KR87.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Conformal; Laminations; Quasiconformal; Weldings
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Makarov, Nikolai G.
Thesis Committee:
  • Makarov, Nikolai G. (chair)
  • Calegari, Danny C.
  • Hersonsky, Saar
  • Schlag, Wilhelm
Defense Date:10 July 2003
Record Number:CaltechETD:etd-05132004-233348
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1772
Deposited By: Imported from ETD-db
Deposited On:14 May 2004
Last Modified:20 Jan 2021 22:54

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