We study a generalization of the geodesic spray and give conditions for noncomapct manifolds with a Lie structure at infinity to have positive injectivity radius. We also prove that the geometricâ€¦ (More)

We study some basic analytic questions related to differential operators on Lie manifolds, which are manifolds whose large scale geometry can be described by a a Lie algebra of vector fields on aâ€¦ (More)

We prove a surgery formula for the smooth Yamabe invariant Ïƒ(M) of a compact manifold M . Assume that N is obtained from M by surgery of codimension at least 3. We prove the existence of a positiveâ€¦ (More)

Let M be a compact manifold equipped with a Riemannian metric g and a spin structure Ïƒ. We let Î»+min(M, [g], Ïƒ) = inf gÌƒâˆˆ[g] Î» + 1 (gÌƒ)V ol(M, gÌƒ) 1/n where Î»+1 (gÌƒ) is the smallest positiveâ€¦ (More)

We prove a regularity result for the Poisson problem âˆ’âˆ†u = f , u|âˆ‚P = g on a polyhedral domain P âŠ‚ R 3 using the BabuÅ¡kaâ€“Kondratiev spaces Ka (P). These are weighted Sobolev spaces in which theâ€¦ (More)

We show that solutions of the Yamabe equation on certain ndimensional non-compact Riemannian manifolds which are bounded and Lp for p = 2n/(nâˆ’2) are also L2. This Lp-L2-implication provides explicitâ€¦ (More)

Let (M, g) be a compact connected spin manifold of dimension n â‰¥ 3 whose Yamabe invariant is positive. We assume that (M, g) is locally conformally flat or that n âˆˆ {3, 4, 5}. According to a positiveâ€¦ (More)

We study the complex powers A z of an elliptic, strictly positive pseudodifferential operator A using an axiomatic method that combines the approaches of Guillemin and Seeley. In particular, weâ€¦ (More)

It has recently been conjectured that the eigenvalues Î» of the Dirac operator on a closed Riemannian spin manifold M of dimension n â‰¥ 3 can be estimated from below by the total scalar curvature: Î» 2â€¦ (More)

We compute the spectrum of the Dirac operator on 3-dimensional Heisenberg manifolds. The behavior under collapse to the 2-torus is studied. Depending on the spin structure either all eigenvalues tendâ€¦ (More)