Philippe Castillon

Harmonic manifolds are those Riemannian manifolds whose harmonic functions satisfy the mean-value property, or equivalently, whose spheres have constant mean curvature. F. Ledrappier introduced an asymptotic version of harmonicity which was mainly...

We shall see how the positivity of some Schrodinger operator on a surface gives information on its topology and its conformal type. The potent of the operators considered here involve the curvature of the surface and appear naturally in the study of...

The Gauss curvature of a convex body can be seen as a measure on the unit sphere (with some properties). For such a measure \mu , Alexandrov problem consists in proving the existence of a convex body whose curvature measure is \mu . In the Euclidean...