# Members & Guests

Ludwig-Maximilians-Universität München

Telephone: +49 89 2180-4621
Homepage: http://www.mathematik.uni-muenchen.de/~s...

## Project

24Minimal 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):
24Minimal 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):
24Minimal surfaces in metric spaces

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

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

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