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Yannick Krifka

Publications and source records attributed to Yannick Krifka.

4 recordsLinked to original sources
arXiv2024

A non-compact convex hull in generalized non-positive curvature

In this article, we are interested in metric spaces that satisfy a weak non-positive curvature condition in the sense that they admit a conical geodesic bicombing. We show that the analog of a question of Gromov about compactness properties of convex hulls has a negative answer in this setting. Specifically, we prove that there exists a complete metric space $X$ that admits a conical bicombing $σ$ such that $X$ has a finite subset whose closed $σ$-convex hull is not compact.

math.MG↗
arXiv2022

Volume bounds for the canonical lift complement of a random geodesic

Given a filling primitive geodesic curve in a closed hyperbolic surface one obtains a hyperbolic three-manifold as the complement of the curve's canonical lift to the projective tangent bundle. In this paper we give the first known lower bound for the volume of these manifolds in terms of the length of generic curves. We show that estimating the volume from below can be reduced to a counting problem in the unit tangent bundle and solve it by applying an exponential multiple mixing result for the geodesic flow.

math.GT↗
arXiv2020

On the IRS compactification of moduli space

In arXiv:1503.08402v2 Gelander described a new compactification of the moduli space of finite area hyperbolic surfaces using invariant random subgroups. The goal of this paper is to relate this compactification to the classical augmented moduli space, also known as the Deligne-Mumford compactification. We define a continuous finite-to-one surjection from the augmented moduli space to the IRS compactification. The cardinalities of this map's fibers admit a uniform upper bound that depends only on the topology of the underlying surface.

math.GT↗