Holomorphic Cubic Differentials and Minimal Lagrangian Surfaces in CH2
Differential Geometry
2012-01-20 v1 Analysis of PDEs
Abstract
Following earlier work of Loftin-McIntosh, we study minimal Lagrangian immersions of the universal cover of a closed surface (of genus at least 2) into CH2, with prescribed data of a conformal structure plus a holomorphic cubic differential. We show existence and non-uniqueness of such minimal Lagrangian immersions. We also establish the surface area with respect to the induced metric as a Weil-Petersson potential function for the space of holomorphic cubic differentials on the Riemann surface.
Cite
@article{arxiv.1201.3941,
title = {Holomorphic Cubic Differentials and Minimal Lagrangian Surfaces in CH2},
author = {Zheng Huang and John Loftin and Marcello Lucia},
journal= {arXiv preprint arXiv:1201.3941},
year = {2012}
}
Comments
20 pages