4 papers · 1 filter
Second-order rigidity of coned polytope frameworks and the stress-flex conjecture from a vector-valued Schläfli formula
Eleni Pachyli, Roman Prosanov, Martin Winter
A coned polytope framework (CPF) is the bar-joint framework obtained from the 1-skeleton of a convex polytope by coning over some interior point. It was recently shown that CPFs ar…
Polyhedral surfaces in flat (2+1)-spacetimes and balanced cellulations on hyperbolic surfaces
François Fillastre, Roman Prosanov
We first prove that given a hyperbolic metric on a closed surface , any flat metric on with negative singular curvatures isometrically embeds as a convex polyhedral Cauc…
Prescribed curvature problem for discrete conformality on convex spherical cone-metrics
Ivan Izmestiev, Roman Prosanov, Tianqi Wu
Let be the 2-sphere and be a finite set of at least three points. We show that for each function satisfying elementary necessary condit…
Dual metrics on the boundary of strictly polyhedral hyperbolic 3-manifolds
Roman Prosanov
Let be a compact oriented 3-manifold with non-empty boundary consisting of surfaces of genii such that the interior of is hyperbolizable. We show that for each spheric…