Scalar curvature, mass, and harmonic maps

Abstract: For a 3-dimensional Riemannian manifold there is a relationship between the level sets of a harmonic map and the manifold's scalar curvature, expressed by a formula discovered by Daniel Stern. New proofs of classical facts in the study of scalar curvature can be given with this formula. We adopt this harmonic map perspective to give novel bounds for the mass of asymptotically flat initial data sets in terms of certain asymptotically linear functions. As a consequence, we obtain a new proof of the space-time Positive Mass Theorem in dimension 3. These results are joint work with Hugh Bray, Sven Hirsch, Marcus Khuri, and Daniel Stern.

algebraic topologydifferential geometrygeometric topologyK-theory and homology

Audience: researchers in the topic

Göttingen topology and geometry seminar

Series comments: Our seminar takes place via zoom every Tuesday afternoon (Central European Summer Time; the precise time slot varies—please always refer to the listing).