Abstract:In this paper we prove two results on algebraic flows on Shimura varieties. One is the so-called 'logarithmic' Ax-Lindemann theorem. The other concerns the closure of the image of a totally geodesic s...In this paper we prove two results on algebraic flows on Shimura varieties. One is the so-called 'logarithmic' Ax-Lindemann theorem. The other concerns the closure of the image of a totally geodesic sub-variety of a symmetric space by the uniformisation map.Read More