dc.contributor.advisor Wolf, Michael Li, Qiongling 2016-01-25T15:27:41Z 2016-01-25T15:27:41Z 2014-12 2014-12-04 December 2014 Li, Qiongling. "Hitchin Components, Riemannian Metrics and Asymptotics." (2014) Diss., Rice University. https://hdl.handle.net/1911/88090. https://hdl.handle.net/1911/88090 Higher Teichm\"uller spaces are deformation spaces arising from subsets of the space of representations of a surface group into a general Lie group, e.g., $$PSL(n,\RR)$$, which share some of the properties of classical Teichmueller space. By the non-abelian Hodge theory, such representation spaces correspond to the space of Higgs bundles. We focus on two aspects on the Higher Teichm\"uller space: Riemannian geometry and dynamics. First, we construct a new Riemannian metric on the deformation space for $$PSL(3,\RR)$$, and then prove Teichmueller space endowed with Weil-Petersson metric is totally geodesic in deformation space for $$PSL(3,\RR)$$ with the new metric. Secondly, in a joint work with Brian Collier, we are able to obtain asymptotic behaviors and related properties of representations for certain families of Higgs bundles of rank n. application/pdf eng Hitchin ComponentsHiggs Bundles Hitchin Components, Riemannian Metrics and Asymptotics Thesis Hardt, Robert Gillman, Adrianna 2016-01-25T15:27:41Z Text Mathematics Natural Sciences Rice University Doctoral Doctor of Philosophy
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