Florian Frick

activity

20232026

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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.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

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.MG2023

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…