Holomorphic Cubic Differentials and Minimal Lagrangian Surfaces in CH2

2012/01/18 by Huang, Zheng, Loftin, John, Lucia, Marcello
#53C42 (Primary) 35J61 #53D12 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.3941

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.

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