File(s) under embargo

113

days

23

hours

until file(s) become available

Harmomic maps into Teichmuller spaces and superrigidity of mapping class groups

thesis
posted on 15.05.2020, 02:20 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

Licence

Exports

Licence

Exports