In particular Lopez  proved that the only minimal translation surfaces in hyperbolic space are totally geodesic planes.
Zafindratafa, A generalization of the translation surfaces of Scherk, Diff.
Jiu, Translation surfaces with constant mean curvature in 3-dimensional spaces, J.
Lopez, Minimal translation surfaces in hyperbolic space, To appear in Contributions to Algebra and Geometry.
Some of the topics include ergodic natural measures, odometers and Toeplitz flows, an approach to non-singular entropy, the exactness of Rokhlin endomorphisms and weak mixing of Poisson boundaries, elements of the theory of unimodular Pisot substitutions with an application to beta-shifts, anisotropic Sobolev spaces and dynamical transfer operators, Hausdorff dimensions for Martin metrics, twistwise flow equivalence (and beyond), dynamical zeta functions and symplectic Floer homology, periodic geodesics on genetic translation surfaces
, actions in the infinite-dimensional nilpotent group, orbit counting, spaces of elliptic differentials, and interactions between dynamics, arithmetics and combinatorics (the good, the bad and the ugly).