Publications of SPP2026
On this site you find preprints and publications produced within the projects and with the support of the DFG priority programme „Geometry at Infinity“.
- all projects
- 01Hitchin components for orbifolds
- 02Asymptotic geometry of sofic groups and manifolds
- 03Geometric operators on a class of manifolds with bounded geometry
- 04Secondary invariants for foliations
- 05Index theory on Lorentzian manifolds
- 06Spectral Analysis of Sub-Riemannian Structures
- 07Asymptotic geometry of moduli spaces of curves
- 08Parabolics and invariants
- 09Diffeomorphisms and the topology of positive scalar curvature
- 10Duality and the coarse assembly map
- 11Topological and equivariant rigidity in the presence of lower curvature bounds
- 12Anosov representations and Margulis spacetimes
- 13Analysis on spaces with fibred cusps
- 14Boundaries of acylindrically hyperbolic groups and applications
- 15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds
- 16Minimizer of the Willmore energy with prescribed rectangular conformal class
- 17Existence, regularity and uniqueness results of geometric variational problems
- 18Analytic L2-invariants of non-positively curved spaces
- 19Boundaries, Greens formulae and harmonic functions for graphs and Dirichlet spaces
- 20Compactifications and Local-to-Global Structure for Bruhat-Tits Buildings
- 21Stability and instability of Einstein manifolds with prescribed asymptotic geometry
- 22Willmore functional and Lagrangian surfaces
- 23Spectral geometry, index theory and geometric flows on singular spaces
- 24Minimal surfaces in metric spaces
- 25The Willmore energy of degenerating surfaces and singularities of geometric flows
- 26Projective surfaces, Segre structures and the Hitchin component for PSL(n,R)
- 27Invariants and boundaries of spaces
- 28Rigidity, deformations and limits of maximal representations
- 29Curvature flows without singularities
- 30Nonlinear evolution equations on singular manifolds
- 31Solutions to Ricci flow whose scalar curvature is bounded in Lp.
- 32Asymptotic geometry of the Higgs bundle moduli space
- 33Gerbes in renormalization and quantization of infinite-dimensional moduli spaces
- 34Asymptotic geometry of sofic groups and manifolds II
- 35Geometric operators on singular domains
- 36Cohomogeneity, curvature, cohomology
- 37Boundary value problems and index theory on Riemannian and Lorentzian manifolds
- 38Geometry of surface homeomorphism groups
- 39Geometric invariants of discrete and locally compact groups
- 40Construction of Riemannian manifolds with scalar curvature constraints and applications to general relativity
- 41Geometrically defined asymptotic coordinates in general relativity
- 42Spin obstructions to metrics of positive scalar curvature on nonspin manifolds
- 43Singular Riemannian foliations and collapse
- 44Actions of mapping class groups and their subgroups
- 45Macroscopic invariants of manifolds
- 46Ricci flows for non-smooth spaces, monotonic quantities, and rigidity
- 47Self-adjointness of Laplace and Dirac operators on Lorentzian manifolds foliated by noncompact hypersurfaces
- 48Profinite and RFRS groups
- 49Analysis on spaces with fibred cusps II
- 50Probabilistic and spectral properties of weighted Riemannian manifolds with Kato bounded Bakry-Emery-Ricci curvature
- 51The geometry of locally symmetric manifolds via natural maps
- 52Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds II
- 53Gauge-theoretic methods in the geometry of G2-manifolds
- 54Cohomology of symmetric spaces as seen from infinity
- 55New hyperkähler spaces from the the self-duality equations
- 56Large genus limit of energy minimizing compact minimal surfaces in the 3-sphere
- 57Existence, regularity and uniqueness results of geometric variational problems II
- 58Profinite perspectives on l2-cohomology
- 59Laplacians, metrics and boundaries of simplicial complexes and Dirichlet spaces
- 60Property (T)
- 61At infinity of symmetric spaces
- 62A unified approach to Euclidean buildings and symmetric spaces of noncompact type
- 63Uniqueness in mean curvature flow
- 64Spectral geometry, index theory and geometric flows on singular spaces II
- 65Resonances for non-compact locally symmetric spaces
- 66Minimal surfaces in metric spaces II
- 67Asymptotics of singularities and deformations
- 68Minimal Lagrangian connections and related structures
- 69Wall-crossing and hyperkähler geometry of moduli spaces
- 70Spectral theory with non-unitary twists
- 71Rigidity, deformations and limits of maximal representations II
- 72Limits of invariants of translation surfaces
- 73Geometric Chern characters in p-adic equivariant K-theory
- 74Rigidity, stability and deformations in nearly parallel G2-geometry
- 75Solutions to Ricci flow whose scalar curvature is bounded in L^p II
- 76Singularities of the Lagrangian mean curvature flow
- 77Asymptotic geometry of the Higgs bundle moduli space II
- 78Duality and the coarse assembly map II
- 79Alexandrov geometry in the light of symmetry and topology
- 80Nonlocal boundary problems: Index theory and semiclassical asymptotics
We prove regularity estimates for the eigenfunctions of Schrödinger type operators whose potentials have inverse square singularities and uniform radial limits at infinity. In particular, the usual N-body operators are covered by our result; in that case, the weight is in terms of the (euclidean) distance to the collision planes. The technique of proof is based on blow-ups and Lie manifolds. More precisely, we first blow-up the spheres at infinity of the collision planes to obtain the Georgescu-Vasy compactification and then we blow-up the collision planes. We carefully investigate how the Lie manifold structure and the associated data (metric, Sobolev spaces, differential operators) change with each blow-up. Our method applies also to higher order operators and matrices of scalar operators.
| Journal | to appear in Letters Math. Phys. |
| Link to preprint version |
Related project(s):
35Geometric operators on singular domains
Let (N,h) be a time- and space-oriented Lorentzian spin manifold, and let M be a compact spacelike hypersurface of N with induced Riemannian metric g and second fundamental form K. If (N,h) satisfies the dominant energy condition in a strict sense, then the Dirac-Witten operator of M⊂ N is an invertible, self-adjoint Fredholm operator. This allows us to use index theoretical methods in order to detect non-trivial homotopy groups in the space of initial data pairs on $M$ satisfying the dominant energy condition in a strict sense. The central tool will be a Lorentzian analogue of Hitchin's α-invariant. In case that the dominant energy condition only holds in a weak sense, the Dirac-Witten operator may be non-invertible, and we will study the kernel of this operator in this case.
We will show that the kernel may only be non-trivial if π1(M) is virtually solvable of derived length at most 2. This allows to extend the index theoretical methods to spaces of initial data pairs, satisfying the dominant energy condition in the weak sense.
We will show further that a spinor φ is in the kernel of the Dirac--Witten operator on (M,g,K) if and only if (M,g,K,φ) admits an extension to a Lorentzian manifold (N,h) with parallel spinor ψ such that M is a Cauchy hypersurface of (N,h), such that g and K are the induced metric and second fundamental form of M, respectively, and φ is the restriction of ψ to M.
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Related project(s):
35Geometric operators on singular domains