Faculté des sciences et de médecine

Ideal polyhedral surfaces in Fuchsian manifolds

Prosanov, Roman

In: Geometriae Dedicata, 2020, vol. 206, no. 1, p. 151–179

Let Sg,n be a surface of genus g>1 with n>0 punctures equipped with a complete hyperbolic cusp metric. Then it can be uniquely realized as the boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a new variational proof of this result. We also give an alternative proof of the existence and uniqueness of a hyperbolic polyhedral metric with prescribed curvature in a... More

Add to personal list
    Summary
    Let Sg,n be a surface of genus g>1 with n>0 punctures equipped with a complete hyperbolic cusp metric. Then it can be uniquely realized as the boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a new variational proof of this result. We also give an alternative proof of the existence and uniqueness of a hyperbolic polyhedral metric with prescribed curvature in a given conformal class.