First variation of the mass of a closed Riemannian manifold

12.01.2017, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.12
Forschungsseminar Differentialgeometrie

Andreas Hermann

Let (M,g) be a closed Riemannian manifold such that all eigenvalues of the conformal Laplace operator L_g are strictly positive and such that g is flat on an open neighborhood of a point p. The constant term in the expansion of the Green function of L_g at p is called the mass of (M,g) at p.
In this talk we investigate the dependence of the mass on the Riemannian metric. We compute the first variation of the mass with respect to a change of metric and we discuss critical points of the mass. This is joint work with Emmanuel Humbert.