Abstract: We discuss the preservation of concavity under the porous medium flow on a Riemannian manifold, and clarify the effects of the diffusion nonlinearity and the curvature. In particular,  we establish curvature obstructions: If the sectional curvature is always nonpositive and its minimum value is negative at some point,
then any concavity is not preserved. More generally, if the sectional curvature is nonzero somewhere, then any preserved concavity must be stronger than the concavity associated with the diffusion nonlinearity. This talk is based on joint work with Kazuhiro Ishige and Yoshiumi Tateoka.

For further information please contact elisur.magrini@unibocconi.it