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SumTopo 2001, Sixteenth Summer Conference on Topology and its Applications
July 18-21, 2001
City College of CUNY
New York, NY, USA

Organizers
Ralph Kopperman (City College, CUNY), Susan Andima (CW Post College, LIU), Gerald Itzkowitz (Queens College, CUNY), Prabudh Misra (College of Staten Island, CUNY), Shelly Rothman (CW Post College, LIU), Aaron Todd (Baruch College, CUNY)

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Complex Earthquakes are Analytic
by
Dragomir Saric
The Graduate Center of The CUNY

Dragomir Saric

Title: “Complex Earthquakes are Holomorphic”

Abstract. We give the definition of a finite earthquake and some examples. Then we define a general earthquake. Earthquakes extend to homeomorphisms of the unit circle and vice versa any homeomorphism of the unit circle is the restriction of an earthquake. There is an earthquake measure corresponding to any earthquake. A general measure may not yield an earthquake but a bounded measure does. Since the measure t is bounded if is bounded, the curve of earthquakes corresponding to t is an earthquake path. In the end we show that bounded earthquake measures correspond to quasisymmetric homemorphisms. Moreover, the earthquake path extends to a holomorphic motion defined in a domain D() containing the real axis.

Date received: July 3, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahy-07.