Almost-Fuchsian representations in PU(2,1)
Differential Geometry
2026-03-02 v3 Functional Analysis
Geometric Topology
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)
Cite
@article{arxiv.2411.16261,
title = {Almost-Fuchsian representations in PU(2,1)},
author = {Samuel Bronstein},
journal= {arXiv preprint arXiv:2411.16261},
year = {2026}
}