For d=3 the limit cones of multi-Fuchsian representations can have finitely many sides scaling with genus, dense boundary rays, or vary discontinuously with the representation.
Wienhard , An invitation to higher Teichm\"uller theory, Proceedings of the International Congress of Mathematicians (Rio de Janeiro 2018), vol
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Limit cones of multi-Fuchsian representations
For d=3 the limit cones of multi-Fuchsian representations can have finitely many sides scaling with genus, dense boundary rays, or vary discontinuously with the representation.