3 papers
math.MG2025
Geodesic complexity of the octahedron, and an algorithm for cut loci on convex polyhedra
Florian Frick, Pranav Rajbhandari
The geodesic complexity of a length space quantifies the required number of case distinctions to continuously choose a shortest path connecting any given start and end point. W…
math.CO2025
Covering and labeling generalizations of the Borsuk-Ulam theorem
Florian Frick, Zoe Wellner
We prove multiple generalizations of Fan's combinatorial labeling result for sphere triangulations. This can be seen as a comprehensive extension of the Borsuk--Ulam theorem. In ty…
math.MG2025
Roots of real-valued zero mean maps: Compositions of linear functionals and equivariant maps
Francesca Cantor, Julia D'Amico, Florian Frick +1
We develop a novel topological framework that yields results constraining the distribution of zeros of certain zero mean real-valued maps, namely those obtained from composing a fi…