Quasilinearization and curvature of Aleksandrov spaces

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Weak topologies in complete $CAT(0)$ metric spaces (2012, methodology): “Berg and Nikolaev [2] have introduced the concept of quasilinearization along these lines.”
Convergence rates for the generalized Fréchet mean via the quadruple inequality (2018, background): “on on R2 with mean µ∈Yand Fr´echet mean m∈Qwith respect to the Euclidean metric and the descriptor space Q. The green, blue, and red lines show p (t) for = 0.6,0.3,0. 24 can be found in [Bac18]. In [BN08] the authors characterize Hadamard spaces by the nice quadruple inequality and discuss a quasili”
Nonpositive Curvature and the Ptolemy Inequality (2007, background): “[2], a recent joint work of Berg and Nikolaev.”
The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces (2012, background): “s equivalent to d2(x 1,x2) +d 2(x 2,x3)+d 2(x 3,x4) +d 2(x 4,x1)−d 2(x 1,x3) −d 2(x 2,x4) ≥ 0 (7.13) for all quadruples (x1,x2,x3,x4) ∈ X4. According to a recent characterization by Berg and Nikolaev [BN08], for a geodesic mm-space this in turn is equivalent to nonpositive curvature in the sense of ”