Maung Min-Oo

Scalar curvature rigidity of asymptotically hyperbolic spin manifolds

In this paper we study the hyperbolic version of this result using Wittens method and show that a spin manifold which is (strongly) asymptotically hyperbolic cannot have scalar curvature R≥ = −n(n−1) everywhere unless it is isometric to hyperbolic space

Calibrated Subbundles in Noncompact Manifolds of Special Holonomy

This paper is a continuation of Math. Res. Lett.12 (2005), 493–512. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of Sn by looking at the conormal bundle of appropriate submanifolds of Sn. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey–Lawson for submanifolds in Rn in their pioneering paper, Acta Math. 148 (1982), 47–157. We also construct calibrated submanifolds in complete metrics with special holonomy G2 and Spin(7) discovered by Bryant and Salamon (Duke Math. J. 58 (1989), 829–850) on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds in a compact manifold with special holonomy.

A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.