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 that the normal metric on the homogeneous space E7/PSO(8) is stable
with respect to the Einstein-Hilbert action, thereby exhibiting the first
known example of a non-symmetric metric of positive scalar curvature with this property.
Related project(s):
74Rigidity, stability and deformations in nearly parallel G2-geometry
In this article we study the stability problem for the Einstein metrics on
Sasaki Einstein and on complete nearly parallel G2 manifolds. In the Sasaki
case we show linear instability if the second Betti number is positive.
Similarly we prove that nearly parallel G2 manifolds with positive third
Betti number are linearly unstable. Moreover, we prove linear instability
for the Berger space SO(5)/SO(3)_irr which is a 7-dimensional homology
sphere with a proper nearly parallel G2 structure.
| Journal | to appear in Int. J. Math. |
| Link to preprint version |
Related project(s):
74Rigidity, stability and deformations in nearly parallel G2-geometry
In this article we study the stability problem for the Einstein-Hilbert functional on compact symmetric spaces following and completing the seminal work of Koiso on the subject. We classify in detail the irreducible representations of simple Lie algebras with Casimir eigenvalue less than the Casimir eigenvalue of the adjoint representation, and use this information to prove the stability of the Einstein metrics on both the quaternionic and Cayley projective plane. Moreover we prove that the Einstein metrics on quaternionic Grassmannians different from projective spaces are unstable.
| Journal | J. Geom. Anal. (2022) 32:137 |
| Link to preprint version |
Related project(s):
74Rigidity, stability and deformations in nearly parallel G2-geometry
We obtain new lower bounds for the first non-zero eigenvalue of the scalar
sub-Laplacian for 3-Sasaki metrics, improving Lichnerowicz-Obata type
estimates by Ivanov et al. The limiting eigenspace is fully decribed in
terms of the automorphism algebra. Our results can be thought of as an
analogue of the Lichnerowicz-Matsushima estimate for Kähler-Einstein
metrics. In dimension 7, if the automorphism algebra is non-vanishing,
we also compute the second eigenvalue for the sub-Laplacian and construct
explicit eigenfunctions. In addition, for all metrics in the canonical
variation of the 3-Sasaki metric we give a lower bound for the spectrum of the Riemannian Laplace operator, depending only on scalar curvature and dimension.
We also strengthen a result pertaining to the growth rate of harmonic
functions, due to Conlon, Hein and Sun, in the case of hyperkähler
cones. In this setup we also describe the space of holomorphic functions.
Related project(s):
74Rigidity, stability and deformations in nearly parallel G2-geometry
We initiate a systematic study of the deformation theory of the second Einstein
metric \(g_{1/\sqrt{5}}\) respectively the proper nearly G2 structure \(\phi_{1/\sqrt{5}}\) of a 3-Sasaki manifold \((M^7,g)\). We show that infinitesimal Einstein deformations for \(g_{1/\sqrt{5}}\) coincide with infinitesimal \(G_2\) deformations for \(\phi_{1/\sqrt{5}}\). The latter are showed to be parametrised by eigenfunctions of the basic Laplacian of g, with eigenvalue twice the Einstein constant of the base 4-dimensional orbifold, via an explicit differential operator. In terms of this parametrisation we determine those infinitesimal \(G_2\) deformations which are unobstructed to second order.
Related project(s):
74Rigidity, stability and deformations in nearly parallel G2-geometry
We describe the second order obstruction to deformation for nearly G_2 structures on compact manifolds. Building on work of B. Alexandrov and U. Semmelmann this allows proving rigidity under deformation for the proper nearly G_2 structure on the Aloff-Wallach space N(1,1).
| Journal | J. London Math. Soc. (2) 104 (2021) 1795--1811 |
| Link to preprint version |
Related project(s):
74Rigidity, stability and deformations in nearly parallel G2-geometry
We show that a strict, nearly Kähler 6-manifold with either second or third Betti number nonzero is linearly unstable with respect to the \(\nu\)-entropy of Perelman and hence is dynamically unstable for the Ricci flow.
| Journal | Ann. Global Anal. Geom. 57 no. 1, 15-22 (2020) |
| Link to preprint version |
Related project(s):
74Rigidity, stability and deformations in nearly parallel G2-geometry