Ahlfors Bers Colloquium

May 19-22, 2005
University of Michigan
Ann Arbor, Michigan

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University of Michigan

Mathematics Department

Organizers
Dick Canary
Juha Heinonen

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Workshop Abstract Detail

Young-Heon Kim Northwestern University

Determinants of Laplacians and their holomorphic extensions We consider the determinant of the Laplacian as a function on the Teichmueller space of a closed surface S of genus >1 and show that it has a unique holomorphic extension to the quasifuchsian space. To realize this holomorphic extension as determinants of actual differential operators on S, we construct holomorphic extensions of Laplace operators of hyperbolic metrics on S using Ahlfors-Bers theory of quasiconformal mappings, and we study their determinants.

Topic: Weil-Petersson Geometry of Teichmuller space