References of "Mondello, Gabriele"
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See detailMinimizing immersions of a hyperbolic surface in a hyperbolic 3-manifold
Bonsante, Francesco; Mondello, Gabriele; Schlenker, Jean-Marc UL

E-print/Working paper (2019)

Let (S,h) be a closed hyperbolic surface and M be a quasi-Fuchsian 3-manifold. We consider incompressible maps from S to M that are critical points of an energy functional F which is homogeneous of degree ... [more ▼]

Let (S,h) be a closed hyperbolic surface and M be a quasi-Fuchsian 3-manifold. We consider incompressible maps from S to M that are critical points of an energy functional F which is homogeneous of degree 1. These ``minimizing'' maps are solutions of a non-linear elliptic equation, and reminiscent of harmonic maps -- but when the target is Fuchsian, minimizing maps are minimal Lagrangian diffeomorphisms to the totally geodesic surface in M. We prove the uniqueness of smooth minimizing maps from (S,h) to M in a given homotopy class. When (S,h) is fixed, smooth minimizing maps from (S,h) are described by a simple holomorphic data on S: a complex self-adjoint Codazzi tensor of determinant 1. The space of admissible data is smooth and naturally equipped with a complex structure, for which the monodromy map taking a data to the holonomy representation of the image is holomorphic. Minimizing maps are in this way reminiscent of shear-bend coordinates, with the complexification of F analoguous to the complex length. [less ▲]

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See detailA cyclic extension of the earthquake flow II
Bonsante, Francesco; Mondello, Gabriele; Schlenker, Jean-Marc UL

in Annales Scientifiques de l'Ecole Normale Supérieure (2015), 48(4), 811859

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See detailA cyclic extension of the earthquake flow I
Bonsante, Francesco; Mondello, Gabriele; Schlenker, Jean-Marc UL

in Geometry and Topology (2013), 17(1), 157--234

Detailed reference viewed: 123 (5 UL)