Harmomic Maps into Teichmuller Spaces and Superrigidity of Mapping Class Groups

Ling Xu, Purdue University

Abstract

This thesis contains two parts. In the first part of the present work, we will study the harmonic maps onto Teichm¨uller space. We will formulate a general Bochner type formula for harmonic maps into Teichm¨uller space. We will also prove the existence theorem of equivariant harmonic maps from a symmetric space with finite volume into its Weil-Petersson completion T , by deforming an almost finite energy map in the sense of [1] into a finite energy map. In the second part of the work, we discuss the superrigidity of mapping class group. We will provide a geometric proof of both the high rank and the rank one superrigidity of mapping class groups due to Farb-Masur [2] and Yeung [3].

Degree

Ph.D.

Advisors

Yeung, Purdue University.

Subject Area

Energy|Mathematics

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