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Necessary and sufficient conditions are obtained for the infinitesimal rigidity of braced grids in the plane with respect to non-Euclidean norms. Component rectangles of the grid may carry 0, 1 or 2 diagonal braces, and the combinatorial part of the conditions is given in terms of a matroid for the bicoloured bipartite multigraph defined by the braces.
A bar-joint framework $(G,p)$ in a (non-Euclidean) real normed plane $X$ is the combination of a finite, simple graph $G$ and a placement $p$ of the vertices in $X$. A framework $(G,p)$ is globally rigid in $X$ if every other framework $(G,q)$ in $X$
This is a survey on nondiscrete euclidean buildings, with a focus on metric properties of these spaces.
We study the Wasserstein space (with quadratic cost) of Euclidean spaces as an intrinsic metric space. In particular we compute their isometry groups. Surprisingly, in the case of the line, there exists a (unique) exotic isometric flow. This contrast
Four points ordered in the positive order on the unit circle determine the vertices of a quadrilateral, which is considered either as a euclidean or as a hyperbolic quadrilateral depending on whether the lines connecting the vertices are euclidean or
Let $G$ be a $3$-connected graph with $n$ vertices and $m$ edges. Let $mathbf{p}$ be a randomly chosen mapping of these $n$ vertices to the integer range $[1..2^b]$ for $bge m^2$. Let $mathbf{l}$ be the vector of $m$ Euclidean lengths of $G$s edges u