In the study of the regularity of Radon measures tangent measures play a crucial role. One of the key ideas in understanding these tangent objects is the connectivity properties of the cones of measures.
In this talk I will give an overview of these techniques. I will illustrate their use with a couple of applications. We expect these ideas yield insight in problems where the geometry of a measure is in question.
This is joint work with C. Kenig and D. Preiss.