93 citations · 187 across the 31 of their papers we have counts for
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Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings
Giacomo Del Nin, Mircea Petrache
We prove discrete-to-continuum convergence of interaction energies defined on lattices in the Euclidean space (with interactions beyond nearest neighbours) to a crystalline perimet…
Sharp discrete isoperimetric inequalities in periodic graphs via discrete PDE and Semidiscrete Optimal Transport
Mircea Petrache, Matias Gomez
We develop criteria based on a calibration argument via discrete PDE and semidiscrete optimal transport, for finding sharp isoperimetric inequalities of the form $(\sharp Ω)^{d-1}…
Coefficient groups inducing nonbranched optimal transport
Mircea Petrache, Roger Züst
In this work we consider an optimal transport problem with coefficients in a normed Abelian group , and extract a purely intrinsic condition on that guarantees that the opti…
Matchings in metric spaces, the dual problem and calibrations modulo 2
Mircea Petrache, Roger Züst
We show that for a metric space with an even number of points there is a 1-Lipschitz map to a tree-like space with the same matching number. This result gives the first basic versi…