On Geodesies in Infinite Dimensional Teichmuller Spaces

It is well known that a finite dimensional Teichmuller space is a straight geodesicspace in the sense of Buseman (S .Kravetz 1]); roughly speaking, that is, for anypair of points in a finite dimensional Teichmuller space, there is a unique geodesicline through them. But we do not know whether or not the same is true for the in-finite dimension case.