On the positive mass conjecture for closed Riemannian manifolds

26.05.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Andreas Hermann

Let (M,g) be a closed Riemannian manifold such that all eigenvalues of the conformal Laplace operator L_g of 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. It is an open conjecture that under the assumptions above the mass is non-negative and that it is zero if and only if (M,g) is conformally diffeomorphic to the round sphere.
In this talk we introduce the mass of a more general class of elliptic operators of the form \Delta_g+f, where f is a smooth function on M vanishing on an open neighborhood of p, and we discuss some properties of this mass. This is joint work with Emmanuel Humbert.