Díaz Sánchez, RaquelSeries, Caroline2023-06-202023-06-2020031472-2747https://hdl.handle.net/20.500.14352/57389Given two measured laminations µ and ν in a hyperbolic sur-face which fill up the surface, Kerckhoff defines an associated line of minima along which convex combinations of the length functions of µ andν are minimised. This is a line in Teichmüller space which can be thought as analogous to the geodesic in hyperbolic space determined by two points at infinity. We show that when µ is uniquely ergodic, this line converges to the projective lamination [µ], but that when µ is rational, the line converges not to [µ], but rather to the barycentre of the support of µ. Similar results on the behaviour of Teichmüller geodesics have been proved by Masurengjournal articlehttp://emis.math.ca/journals/UW/agt/ftp/main/2003/agt-3-9.pdfhttp://emis.org/open access514Moduli of Riemann surfacesTeichmüller theoryFuchsian groups and their generalizationsQuasiconformal methods and Teichmüller theoryFuchsian and Kleinian groups as dynamical systemsGeometric structures on low-dimensional manifoldsGeometría1204 Geometría