## Welcome to SPP 2026

This is the platform of a coordinated research programme in mathematics, funded by the German Research Foundation (DFG). It comprises 33 research projects in the fields of differential geometry, geometric topology, and global analysis. More than 80 researchers from doctoral to professorial level and based at more than 20 German and Swiss universities are represented in this programme.

### Research projects for second funding period

DFG granted 46 research proposals for the second funding period of SPP 2026 (2020-2023).

## Latest publications

#### Maximal metric surfaces and the Sobolev-to-Lipschitz property

Paul Creutz and Elefterios Soultanis

We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by…

#### Plateau's problem for singular curves

Paul Creutz

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…

#### The Plateau-Douglas problem for singular configurations and in general metric spaces

Paul Creutz and Martin Fitzi

Assume you are given a finite configuration $\Gamma$ of disjoint rectifiable Jordan curves in $\mathbb{R}^n$. The Plateau-Douglas problem asks whether…

#### The branch set of minimal disks in metric spaces

Paul Creutz and Matthew Romney

We study the structure of the branch set of solutions to Plateau's problem in metric spaces satisfying a quadratic isoperimetric inequality. In our…

## Latest Blog posts

**Breakthrough Prizes 2021**Three days ago the Breakthrough Prize Foundation announced the recipients of the 2021 Breakthrough Prizes. I focus in this post only on the prizes in mathematics (there are also prizes in life sciences and physics). Martin Hairer is the recipient of the 2021 Breakthrough Prize in Mathematics for transformative contributions to the theory of stochastic … Continue reading "Breakthrough Prizes 2021"

**Contractible 3-manifolds and positive scalar curvature, II**Let \((M,g)\) be a complete, contractible Riemannian \(3\)-manifold (without boundary). Chang-Weinberger-Yu (link) proved that if \((M,g)\) has uniformly positive scalar curvature, then \(M\) must be homeomorphic to \(\mathbb{R}^3\). Recently (arXiv:1906.04128), Wang proved that if \((M,g)\) has positive scalar curvature and \(M\) has trivial fundamental group at infinity, then \(M\) must be homeomorphic to \(\mathbb{R}^3\). Jiang … Continue reading "Contractible 3-manifolds and positive scalar curvature, II"

**Isometry groups of hyperbolic surfaces**A month ago Aougab, Patel and Vlamis posted a preprint on the arXiv (arXiv:2007.01982) about the question which groups, for a fixed orientable surface of infinite genus, can be realized as the full isometry group of a Riemannian metric of constant negative curvature on that surface. To my surprise, they stated in the introduction that … Continue reading "Isometry groups of hyperbolic surfaces"