79 citations · 378 across the 29 of their papers we have counts for
30 papers
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…
On the geometry and topology of initial data sets with horizons
Lars Andersson, Mattias Dahl, Gregory J. Galloway +1
We study the relationship between initial data sets with horizons and the existence of metrics of positive scalar curvature. We define a Cauchy Domain of Outer Communications (CDOC…
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…
A non-existence result for a generalization of the equations of the conformal method in general relativity
Mattias Dahl, Romain Gicquaud, Emmanuel Humbert
The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admi…
Low-dimensional surgery and the Yamabe invariant
Bernd Ammann, Mattias Dahl, Emmanuel Humbert
Assume that M is a compact n-dimensional manifold and that N is obtained by surgery along a k-dimensional sphere, k\le n-3. The smooth Yamabe invariants σ(M) and σ(N) satisfy σ(N)\…
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…
A limit equation associated to the solvability of the vacuum Einstein constraint equations using the conformal method
Mattias Dahl, Romain Gicquaud, Emmanuel Humbert
Let be a compact Riemannian manifold on which a trace-free and divergence-free and a positive function , , are fixed. In this paper, we…
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…