Florian Frick

collaborators

4 papers

math.MG2026

Gromov-Hausdorff distance and Jung constant of finite-dimensional normed spaces

Henry Adams, Semeon A. Bogatyi, Florian Frick +5

For a finite-dimensional normed space $V$ and a subset $X$ with finite Hausdorff distance from $V$ , we prove that the Gromov--Hausdorff distance between $X$ and $V$ is at least the…

math.MG2026

Quantifying discontinuity

Henry Adams, Florian Frick, Michael Harrison +2

Given a compact space $X$ that does not admit an embedding (an injective continuous function) into $R^{d}$ , we study the ''degree'' of discontinuity that any injective funct…

math.MG2025

An optimal Brouwer's fixed point theorem for discontinuous functions

Henry Adams, Florian Frick

Brouwer's fixed point theorem states that any continuous function from a closed $n$ -dimensional ball to itself has a fixed point. In 1961, Klee showed that if such a function has d…

math.MG2025

Hausdorff vs Gromov-Hausdorff distances

Henry Adams, Florian Frick, Sushovan Majhi +1

Let $M$ be a closed Riemannian manifold and let $X \subseteq M$ . If the sample $X$ is sufficiently dense relative to the curvature of $M$ , then the Gromov-Hausdorff distance between…