5 citations · 16 across the 12 of their papers we have counts for
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The Regge symmetry, confocal conics, and the Schläfli formula
Arseniy Akopyan, Ivan Izmestiev
The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asympt…
Statics and kinematics of frameworks in Euclidean and non-Euclidean geometry
Ivan Izmestiev
This is a survey article on the infinitesimal rigidity of frameworks in Euclidean, hyperbolic, and spherical geometry. We discuss the equivalence of the static and kinematic formul…
Spherical and hyperbolic conics
Ivan Izmestiev
This is a survey of metric properties of non-Euclidean conics, mainly based on works of Chasles and Story. A spherical conic is the intersection of the sphere with a quadratic cone…
A general discrete Wirtinger inequality and spectra of discrete Laplacians
Ivan Izmestiev
We prove an inequality that generalizes the Fan-Taussky-Todd discrete analog of the Wirtinger inequality. It is equivalent to an estimate on the spectral gap of a weighted discrete…
Projective background of the infinitesimal rigidity of frameworks
Ivan Izmestiev
We present proofs of two classical theorems. The first one, due to Darboux and Sauer, states that infinitesimal rigidity is a projective invariant; the other one establishes relati…