## 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“.

We present a new technique that employs partial differential equations in order to explicitly construct primitives in the continuous bounded cohomology of Lie groups. As an application, we prove a vanishing theorem for the continuous bounded cohomology of SL(2,R) in degree 4, establishing a special case of a conjecture of Monod.

Journal | Geometry & Topology |

Volume | 19 |

Pages | 3603–3643 |

Link to preprint version | |

Link to published version |

**Related project(s):****27**Invariants and boundaries of spaces

Let \(M^n, n \in \{4,5,6\}\), be a compact, simply connected *n*-manifold which admits some Riemannian metric with non-negative curvature and an isometry group of maximal possible rank. Then any smooth, effective action on \(M^n\) by a torus \(T^{n-2}\) is equivariantly diffeomorphic to an isometric action on a normal biquotient. Furthermore, it follows that any effective, isometric circle action on a compact, simply connected, non-negatively curved four-dimensional manifold is equivariantly diffeomorphic to an effective, isometric action on a normal biquotient.

Journal | Math. Z. |

Volume | 276 |

Pages | 133--152 |

Link to preprint version | |

Link to published version |

**Related project(s):****11**Topological and equivariant rigidity in the presence of lower curvature bounds

We give a solution of Plateau's problem for singular curves possibly having self-intersections. The proof is based on the solution of Plateau's problem for Jordan curves in very general metric spaces by Alexander Lytchak and Stefan Wenger and hence works also in a quite general setting. However the main result of this paper seems to be new even in $\mathbb{R}^n$.

Journal | Comm. Anal. Geom. |

Link to preprint version |

**Related project(s):****24**Minimal surfaces in metric spaces