9 citations · 19 across the 4 of their papers we have counts for
5 papers · 1 filter
Macroscopic scalar curvature bounds on graphs
Steve Karam, Stéphane Sabourau
We establish sharp lower bounds for the lengths of balls in the universal covers of finite metric graphs. For a finite connected -regular graph, with and average edge…
Ball growth at all scales in universal covers of short metric graphs
Steve Karam
Let be a connected metric graph of first Betti number , and let be a trivalent graph of the same Betti number with all edges of unit length. We show that if $\tex…
Macroscopic Schoen conjecture for manifolds with non-zero simplicial volume
Florent Balacheff, Steve Karam
We prove that given a hyperbolic manifold endowed with an auxiliary Riemannian metric whose sectional curvature is negative and whose volume is sufficiently small in comparison to…
Length product of homologically independent loops for tori
Florent Balacheff, Steve Karam
We prove that any Riemannian torus of dimension with unit volume admits homologically independent closed geodesics whose length product is bounded from above by .
Short Homotopically independent loops on surfaces
Steve Karam
In this paper, we are interested in short homologically and homotopically independent loops based at the same point on Riemannian surfaces and metric graphs. First, we show that fo…