## Paul Creutz

### Doctoral student

Universität Köln

E-mail: paul.creutz(at)ish.de

Homepage: http://www.mi.uni-koeln.de/~pcreutz/

## Publications

Let $X$ be a Banach space or more generally a complete metric space admitting a conical geodesic bicombing. We prove that every closed $L$-Lipschitz curve $\gamma:S^1\rightarrow X$ may be extended to an $L$-Lipschitz map defined on the hemisphere $f:H^2\rightarrow X$. This implies that $X$ satisfies a quadratic isoperimetric inequality (for curves) with constant $\frac{1}{2\pi}$. We discuss how this fact controls the regularity of minimal discs in Finsler manifolds when applied to the work of Alexander Lytchak and Stefan Wenger.

Journal | Transactions of the American Mathematical Society |

Link to preprint version |

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