Lipschitz retraction of finite subsets of Hadamard spaces

Leonid V. Kovalev

Abstract: Finite subset spaces of a metric space $X$ form a nested sequence under natural isometric embeddings $X=X(1)\subset X(2)\subset\dots$. We prove that this sequence admits Lipschitz retractions $X(n)\to X(n-1)$ when $X$ is an Hadamard space. This retraction generalizes the concept of convex bicombing, which corresponds to the case $n=2$.

ArXiv: 1406.6742