401 citations · 727 across the 45 of their papers we have counts for
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Topological lower bounds for arithmetic networks
Andrei Gabrielov, Nicolai Vorobjov
We prove a complexity lower bound on deciding membership in a semialgebraic set for arithmetic networks in terms of the sum of Betti numbers with respect to "ordinary" (singular) h…
On metrics of curvature 1 with four conic singularities on tori and on the sphere
Alexandre Eremenko, Andrei Gabrielov
We discuss conformal metrics of curvature 1 on tori and on the sphere, with four conic singularities whose angles are multiples of pi/2. Besides some general results we study in de…
Spherical quadrilaterals with three non-integer angles
Alexandre Eremenko, Andrei Gabrielov, Vitaly Tarasov
We classify spherical quadrilaterals up to isometry in the case when one inner angle is a multiple of pi while the other three are not. This is equivalent to classification of Heun…
On topological lower bounds for algebraic computation trees
Nicolai Vorobjov, Andrei Gabrielov
We prove that the height of any algebraic computation tree for deciding membership in a semialgebraic set is bounded from below (up to a multiplicative constant) by the logarithm o…