Almost-Fuchsian representations in PU(2,1)

2024/11/25 by Bronstein, Samuel
#53C07 #53C42 #53C43 #58J60 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2411.16261

Abstract

In this paper, we study nonmaximal representations of surface groups in PU(2,1). In genus large enough, we show the existence of convex-cocompact representations of non-maximal Toledo invariant admitting a unique equivariant minimal surface, which is holomorphic and almost totally geodesic. These examples can be obtained for any Toledo invariant of the form 2-2g +2/3 d, provided g is large compared to d. When d is not divisible by 3, this yields examples of convex-cocompact representations in PU(2,1) which do not lift to SU(2,1)

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