9 citations · 17 across the 5 of their papers we have counts for
7 papers
Harmonic maps from Kähler manifolds
Brice Loustau
This report attempts a clean presentation of the theory of harmonic maps from complex and Kähler manifolds to Riemannian manifolds. After reviewing the theory of harmonic maps betw…
The sum of Lagrange numbers
Jonah Gaster, Brice Loustau
Combining McShane's identity on a hyperbolic punctured torus with Schmutz's work on the Markov Uniqueness Conjecture (MUC), we find that MUC is equivalent to the identity \begin{eq…
Computing harmonic maps between Riemannian manifolds
Jonah Gaster, Brice Loustau, Léonard Monsaingeon
In the previous paper [GLM2018], we showed that the theory of harmonic maps between Riemannian manifolds may be discretized by introducing triangulations with vertex and edge weigh…
Computing discrete equivariant harmonic maps
Jonah Gaster, Brice Loustau, Léonard Monsaingeon
We present effective methods to compute equivariant harmonic maps from the universal cover of a surface into a nonpositively curved space. By discretizing the theory appropriately,…
Bi-Lagrangian structures and Teichmüller theory
Brice Loustau, Andrew Sanders
In this paper, we review or introduce several differential structures on manifolds in the general setting of real and complex differential geometry, and apply this study to Teichmü…
The complex symplectic geometry of the deformation space of complex projective structures
Brice Loustau
This article investigates the complex symplectic geometry of the deformation space of complex projective structures on a closed oriented surface of genus at least 2. The cotangent…
Minimal surfaces and symplectic structures of moduli spaces
Brice Loustau
Given a closed surface S of genus at least 2, we compare the symplectic structure of Taubes' moduli space of minimal hyperbolic germs with the Goldman symplectic structure on the c…