Abstract Using harmonic mean curvature flow, we establish a sharp Minkowski-type lower bound for total of convex surfaces with given area in Cartan-Hadamard $3$-manifolds. This inequality also improves the known estimates hyperbolic $3$-space. As an application, obtain Bonnesen-style isoperimetric distance function nonpositively curved $3$-spaces, via monotonicity results curvature. connection ...

Minkowski Weighted K-Means is a variant of K-Means set in the Minkowski space, automatically computing weights for features at each cluster. As a variant of K-Means, its accuracy heavily depends on the initial centroids fed to it. In this paper we discuss our experiments comparing six initializations, random and five other initializations in the Minkowski space, in terms of their accuracy, proc...

We study the symplectic geometry of the moduli spaces of polygons in the Minkowski 3-space. These spaces naturally carry completely integrable systems with periodic flows. We extend the Gelfand-Tsetlin method to pseudo-unitary groups and show that the action variables are given by the Minkowski lengths of non-intersecting diagonals.

We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σm = {0, ..., m−1} N that are invariant under multiplication by integers. The results apply to the sets {x ∈ Σm : ∀ k, xkx2k · · ·xnk = 0}, where n ≥ 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.