79 citations · 378 across the 29 of their papers we have counts for
25 papers · 1 filter
The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4
Bernd Ammann, Mattias Dahl
Let be a closed connected spin manifold. Index theory provides a topological lower bound on the dimension of the kernel of the Dirac operator which depends on the choice of Rie…
The Volume-Renormalized Mass from a Hamiltonian Perspective
Mattias Dahl, Klaus Kroencke, Stephen McCormick
We demonstrate that the volume-renormalized mass for asymptotically hyperbolic manifolds recently introduced by the authors can be deduced from a reduced Hamiltonian perspective. I…
A volume-renormalized mass for asymptotically hyperbolic manifolds
Mattias Dahl, Klaus Kroencke, Stephen McCormick
We define a geometric quantity for asymptotically hyperbolic manifolds, which we call the volume-renormalized mass. It is essentially a linear combination of the ADM mass surface i…
Gravitational instantons with symmetry
Steffen Aksteiner, Lars Andersson, Mattias Dahl +2
Uniqueness results for asymptotically locally flat and asymptotically flat -symmetric gravitational instantons are proved using a divergence identity of the type used in uniqu…
Local and global scalar curvature rigidity of Einstein manifolds
Mattias Dahl, Klaus Kroencke
An Einstein manifold is called scalar curvature rigid if there are no compactly supported volume-preserving deformation of the metric which increase the scalar curvature. We give v…
Outermost apparent horizons diffeomorphic to unit normal bundles
Mattias Dahl, Eric Larsson
Given a submanifold of codimension at least three, we construct an asymptotically Euclidean Riemannian metric on with nonnegative scalar curva…
Mass-like invariants for asymptotically hyperbolic metrics. Part I: Classification
Julien Cortier, Mattias Dahl, Romain Gicquaud
In this article, we classify the set of asymptotic mass-like invariants for asymptotically hyperbolic metrics. It turns out that the standard mass is just one example among the two…
A density theorem for asymptotically hyperbolic initial data satisfying the dominant energy condition
Mattias Dahl, Anna Sakovich
When working with asymptotically hyperbolic initial data sets for general relativity it is convenient to assume certain simplifying properties. We prove that the subset of initial…
Asymptotically hyperbolic manifolds with small mass
Mattias Dahl, Romain Gicquaud, Anna Sakovich
For asymptotically hyperbolic manifolds of dimension with scalar curvature at least equal to the conjectured positive mass theorem states that the mass is non-negativ…
Invertible Dirac operators and handle attachments on manifolds with boundary
Mattias Dahl, Nadine Große
For spin manifolds with boundary we consider Riemannian metrics which are product near the boundary and are such that the corresponding Dirac operator is invertible when half-infin…
Penrose type inequalities for asymptotically hyperbolic graphs
Mattias Dahl, Romain Gicquaud, Anna Sakovich
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\bH^n$. The graphs are considered as subsets…
Square-integrability of solutions of the Yamabe equation
Bernd Ammann, Mattias Dahl, Emmanuel Humbert
We show that solutions of the Yamabe equation on certain n-dimensional non-compact Riemannian manifolds which are bounded and L^p for p=2n/(n-2) are also L^2. This L^p-L^2-implicat…
The conformal Yamabe constant of product manifolds
Bernd Ammann, Mattias Dahl, Emmanuel Humbert
Let (V,g) and (W,h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V x W, g+h) in terms…
Mass endomorphism, surgery and perturbations
Bernd Ammann, Mattias Dahl, Andreas Hermann +1
We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass end…
An isoperimetric constant associated to horizons in blown-up at two points
Mattias Dahl, Emmanuel Humbert
Let be a metric on with positive Yamabe constant. When blowing up at two points, a scalar flat manifold with two asymptotically flat ends is produced and this manifol…
Harmonic spinors and local deformations of the metric
Bernd Ammann, Mattias Dahl, Emmanuel Humbert
Let (M,g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this boun…
Smooth Yamabe invariant and surgery
Bernd Ammann, Mattias Dahl, Emmanuel Humbert
We prove a surgery formula for the smooth Yamabe invariant of a compact manifold . Assume that is obtained from by surgery of codimension at least 3. We prove the…
Surgery and the spinorial tau-invariant
Bernd Ammann, Mattias Dahl, Emmanuel Humbert
We associate to a compact spin manifold M a real-valued invariant τ(M) by taking the supremum over all conformal classes over the infimum inside each conformal class of the first p…
Surgery and Harmonic Spinors
Bernd Ammann, Mattias Dahl, Emmanuel Humbert
Let M be a compact manifold with a fixed spin structure χ. The Atiyah-Singer index theorem implies that for any metric g on M the dimension of the kernel of the Dirac operator is b…
On the space of metrics with invertible Dirac operator
Mattias Dahl
On a compact spin manifold we study the space of Riemannian metrics for which the Dirac operator is invertible. The first main result is a surgery theorem stating that such a metri…
Prescribing eigenvalues of the Dirac operator
Mattias Dahl
In this note we show that every compact spin manifold of dimension can be given a Riemannian metric for which a finite part of the spectrum of the Dirac operator consists…
Dirac eigenvalues for generic metrics on three-manifolds
Mattias Dahl
We show that for generic Riemannian metrics on a closed spin manifold of dimension three the Dirac operator has only simple eigenvalues.
Small eigenvalues of the Conformal Laplacian
Christian Baer, Mattias Dahl
We introduce a differential topological invariant for compact differentiable manifolds by counting the small eigenvalues of the Conformal Laplace operator. This invariant vanishes…
Surgery and the Spectrum of the Dirac Operator
Christian Baer, Mattias Dahl
We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension at least 5 the dimension of the space of harmonic spinors is no larger than it m…