2008 DG-MP-PDE Seminar-13

Donaldson introduced a metric and a geometric structure on the space of volume forms on any compact Rimannian manifold. The geodesic equation is a degenerate fully nonlinear elliptic equation. Also this equation is relevant to many interesting problems such as Namh's equation and some interesting free boudary equations. Also the space of volume forms coincides with the conformal class, the probability space. In this talk we try to solve the geodesic equation and its perturbation equation also. This is a joint work with X. Chen.