93 citations · 187 across the 31 of their papers we have counts for
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Crystallization for Coulomb and Riesz Interactions as a Consequence of the Cohn-Kumar Conjecture
Mircea Petrache, Sylvia Serfaty
The Cohn-Kumar conjecture states that the triangular lattice in dimension 2, the lattice in dimension 8, and the Leech lattice in dimension 24 are universally minimizing in t…
Crystallization to the square lattice for a two-body potential
Laurent Bétermin, Lucia De Luca, Mircea Petrache
We consider two-dimensional zero-temperature systems of particles to which we associate an energy of the form where…
Classification of uniformly distributed measures of dimension in general codimension
Paul Laurain, Mircea Petrache
Starting with the work of Preiss on the geometry of measures, the classification of uniform measures in has remained open, except for and for compactly supporte…
Cyclically monotone non-optimal -marginal transport plans and Smirnov-type decompositions for -flows
Mircea Petrache
In the setting of optimal transport with marginals, a necessary condition for transport plans to be optimal is that they are -cyclically monotone. For there exist…
Unconstrained polarization (Chebyshev) problems: basic properties and Riesz kernel asymptotics
Douglas P. Hardin, Mircea Petrache, Edward B. Saff
We introduce and study the unconstrained polarization (or Chebyshev) problem which requires to find an -point configuration that maximizes the minimum value of its potential ove…