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Harmomic maps into Teichmuller spaces and superrigidity of mapping class groups

thesis
posted on 15.05.2020 by Ling Xu
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 $\overline{\mathcal{T}}$, by deforming an almost finite energy map in the sense of Saper 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 and Yeung.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Sai Kee Yeung

Additional Committee Member 2

Laszlo Lempert

Additional Committee Member 3

Donu V.B. Arapura

Additional Committee Member 4

Chi Li

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