<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Loftin, John</style></author><author><style face="normal" font="default" size="100%">McIntosh, Ian</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Minimal Lagrangian surfaces in CH^2 and representations of surface groups into SU(2,1)</style></title><secondary-title><style face="normal" font="default" size="100%">Geometriae Dedicata</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Geometry</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2013</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02/2013</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://front.math.ucdavis.edu/1009.2435</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">162</style></volume><pages><style face="normal" font="default" size="100%">67-93</style></pages><abstract><style face="normal" font="default" size="100%">We use an elliptic differential equation of Tzitzeica type to construct a minimal Lagrangian surface in the complex hyperbolic plane CH^2 from the data of a compact hyperbolic Riemann surface and a small holomorphic cubic differential. The minimal Lagrangian surface is invariant under an SU(2,1) action of the fundamental group. We further parameterise a neighborhood of the R-Fuchsian representations in the representation space by pairs consisting of a point in Teichmuller space and a small cubic differential. By constructing a fundamental domain, we show these representations are complex-hyperbolic quasi-Fuchsian, thus recovering a result of Guichard and Parker-Platis. Our proof involves using the Toda lattice framework to construct an SU(2,1) frame corresponding to a minimal Lagrangian surface. Then the equation of Tzitzeica type is an integrability condition. A very similar equation to ours governs minimal surfaces in hyperbolic 3-space, and our paper can be interpreted as an analog of the theory of minimal surfaces in quasi-Fuchsian manifolds, as first studied by Uhlenbeck.</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><custom1><style face="normal" font="default" size="100%">http://front.math.ucdavis.edu/1009.2435
</style></custom1><section><style face="normal" font="default" size="100%">67</style></section></record></records></xml>