Research Interests for Jeff Jauregui

Almost a century after its introduction, General Relativity continues to produce many interesting geometric problems. Some of the major results in the past few decades are the positive mass theorem and the Penrose inequality, both of which estimate the mass of a spacetime in terms of its geometry. Currently I am studying related inequalities which use curvature data to sharpen the bounds.

The Yamabe Invariant of a smooth manifold is a number, defined geometrically, whose value takes on topological significance. Yamabe invariants have the potential to provide a deeper understanding of the topology of closed 3-manifolds, but they are often very difficult to compute. Recently many surprising connections have been made between Yamabe-like problems and problems in General Relativity. Much of what I study touches on such connections, especially the idea of inverse mean curvature flow.