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
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