Lines of minima and Teichmuller geodesics

For two measured laminations nu(+) and nu(-) that fill up a hyperbolizable surface S and for t epsilon (-infinity, infinity), let L-t be the unique hyperbolic surface that minimizes the length function e(t)l(nu(+)) + e(-t)l(nu(-)) on Teichmuller space. We characterize the curves that are short in Lt and estimate their lengths. We find that the short curves coincide with the curves that are short in the surface g(t) on the Teichmuller geodesic whose horizontal and vertical foliations are respectively, e(t)nu(+) and e(-t)nu(-). By deriving additional information about the twists of nu(+) and nu(-) around the short curves, we estimate the Teichmuller distance between L-t and g(t). We deduce that this distance can be arbitrarily large, but that if S is a once-punctured torus or four-times-punctured sphere, the distance is bounded independently of t.