Purdue_University_Thesis_Template (8).pdf (268.33 kB)

# Harmomic maps into Teichmuller spaces and superrigidity of mapping class groups

thesis
posted on 15.05.2020, 02:20
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.

## Degree Type

Doctor of Philosophy

Mathematics

## Campus location

West Lafayette

Sai Kee Yeung

Laszlo Lempert

Donu V.B. Arapura

Chi Li

## Exports

figshare. credit for all your research.