Extremal k-packings in compact non-orientable surfaces

TL;DR

This paper investigates the maximal arrangements of disjoint metric discs on compact non-orientable surfaces of genus at least 3, focusing on extremal packings that optimize the radius for given topologies.

Contribution

It introduces the concept of extremal k-packings in non-orientable surfaces and analyzes their properties for surfaces with genus g ≥ 3.

Findings

Characterization of extremal k-packings on non-orientable surfaces

Existence results for extremal packings in specified topologies

Insights into the relationship between surface genus and packing configurations

Abstract

An extremal $k$-packing is a collection of $k$ mutually disjoint metric discs, embedded in a surface, whose radius is maximal for the given topology. We study compact non-orientable surfaces of genus $g\ge 3$ containing extremal $k$-packings.