## Dr. Stephan Stadler

### Project leader

Ludwig-Maximilians-Universität München

E-mail: stadler(at)math.lmu.de

Telephone: +49 89 2180-4621

Homepage: http://www.mathematik.uni-muenchen.de/~s…

## Project

**24**Minimal surfaces in metric spaces

## Publications within SPP2026

We prove that a minimal disc in a CAT(0) space is a local embedding away from a finite set of "branch points". On the way we establish several basic properties of minimal surfaces: monotonicity of area densities, density bounds, limit theorems and the existence of tangent maps.

As an application, we prove Fary-Milnor's theorem in the CAT(0) setting.

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

A surface which does not admit a length nonincreasing deformation is called metric minimizing. We show that metric minimizing surfaces in CAT(0) spaces are locally CAT(0) with respect to their intrinsic metric.

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

We prove an analog of Schoen-Yau univalentness theorem for saddle maps between discs.

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

We show that the class of CAT(0) spaces is closed under suitable conformal changes. In particular, any CAT(0) space admits a large variety of non-trivial deformations.

Journal | Math. Ann. |

Volume | Online First |

Link to preprint version |

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