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What is Almost-Fuchsian representations in PU(2,1) about?

In this paper, we study nonmaximal representations of surface groups in PU(2,1). We show the existence in genus large enough, of convex-cocompact representations of nonmaximal Toledo invariant admitting a unique equivariant minimal surface, which is holomorphic and of second fundamental form arbitrarily small. 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).

Author

Bronstein, Samuel

Published

2024

Language

EN