Geometric analysis/Mathematical general relativity: A Positive Mass Theorem for Manifolds with Boundary

  • Date: –16:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Sven Hirsch, Duke University
  • Organiser: Matematiska institutionen
  • Contact person: Stephen McCormick
  • Seminarium

Abstract: One of the central results in mathematical relativity is the positive mass theorem first proven by Richard Schoen and Shing-Tung Yau using minimal surface techniques and later by Edward Witten exploiting the Dirac operator. This result addresses manifolds without boundary which raises the question which information about the mass can be deduced for manifolds with boundary. In the case of an outermost minimal boundary there is the Riemannian Penrose inequality proven by Hubert Bray, Gerhard Huisken and Tom Ilmanen, but for general boundary data much less is known.

We review several results from the literature and present a recent joint work with Pengzi Miao which gives a lower bound on the mass in terms of the mean curvature and gradient of the Green's function at its boundary.