3 papers
math.CO2026
On minimal shapes and isoperimetric constants in hyperbolic lattices
Matteo D'Achille, Vanessa Jacquier, Wioletta M. Ruszel
We fully characterize the set of finite shapes with minimal perimeter on hyperbolic lattices given by regular tilings of the hyperbolic plane whose tiles are regular -gons meeti…
math.PR2026
Isoperimetric inequality for nonlocal bi-axial discrete perimeter
V. Jacquier, W. M. Ruszel, C. Spitoni
In the present manuscript we address and solve for the first time a nonlocal discrete isoperimetric problem. We consider indeed a generalization of the classical perimeter, what we…
math.PR2025
Emergence of metastability on the hyperbolic lattice: Effects of boundary conditions
Vanessa Jacquier, Wioletta M. Ruszel
We investigate the Ising model on finite subgraphs of the hyperbolic lattice under minus boundary conditions and in the presence of a positive external field . Interpreting the…