67 citations · 313 across the 39 of their papers we have counts for
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A Lorentzian analog for Hausdorff dimension and measure
Robert J. McCann, Clemens Sämann
We define a one-parameter family of canonical volume measures on Lorentzian (pre-)length spaces. In the Lorentzian setting, this allows us to define a geometric dimension - akin to…
Classifying minimum energy states for interacting particles: Regular simplices
Cameron Davies, Tongseok Lim, Robert J. McCann
Densities of particles on $\Rn$ which interact pairwise through an attractive-repulsive power-law potential $W_{\al,\bt}(x) = |x|^\al/\al-|x|^\bt/\bt$ have often been used to expla…
Isodiametry, variance, and regular simplices from particle interactions
Tongseok Lim, Robert J McCann
Consider a collection of particles interacting through an attractive-repulsive potential given as a difference of power laws and normalized so that its unique minimum occurs at uni…
Displacement convexity of Boltzmann's entropy characterizes the strong energy condition from general relativity
Robert J McCann
On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstei…