Mattias Dahl

Scalar Curvature Rigidity for Asymptotically Locally Hyperbolic Manifolds

Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The argument is based on a study of the Dirac operator defined with respect to the Killing connection. The existence of asymptotic Killing spinors is related to the spin structure on the end. The expression for the mass is calculated and proven to vanish for conformally compact Einstein manifolds with conformal boundary a spherical space form, giving rigidity. In the four dimensional case, the signature of the manifold is related to the spin structure on the end and explicit formulas for the relevant invariants are given.

Surgery and the spectrum of the Dirac operator

We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension greater than or equal to5 the dimension of the space of harmonic spinors is not larger than it mu ...

A limit equation associated to the solvability of the vacuum Einstein constraint equations by using the conformal method

Let (M, g) be a compact Riemannian manifold on which a trace-free and divergence-free sigma is an element of W-1,W-p and a positive function tau is an element of W-1,W-p, p > n are fixed. In thi ...

Surgery and harmonic spinors

Let M be a compact spin manifold with a chosen spin structure. The Atiyah�Singer index theorem implies that for any Riemannian metric on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending only on M and the spin structure. We show that for generic metrics on M this bound is attained.

Penrose Type Inequalities for Asymptotically Hyperbolic Graphs

In this paper, we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space

Dirac Eigenvalues for Generic Metrics on Three-Manifolds

{\mathbb{H}^n}

Square-integrability of solutions of the Yamabe equation

. The graphs are considered as unbounded hypersurfaces of