5 citations · 12 across the 8 of their papers we have counts for
4 papers · 1 filter
Infinitesimal rigidity of convex surfaces through the second derivative of the Hilbert-Einstein functional II: Smooth case
Ivan Izmestiev
The paper is centered around a new proof of the infinitesimal rigidity of smooth closed surfaces with everywhere positive Gauss curvature. We use a reformulation that replaces defo…
Infinitesimal rigidity of convex surfaces through the second derivative of the Hilbert-Einstein functional I: Polyhedral case
Ivan Izmestiev
The paper is centered around a new proof of the infinitesimal rigidity of convex polyhedra. The proof is based on studying derivatives of the discrete Hilbert-Einstein functional o…
Gauss images of hyperbolic cusps with convex polyhedral boundary
François Fillastre, Ivan Izmestiev
We prove that a 3--dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by its Gauss image. Furthermore, any spherical metric on the torus with cone s…
A variational proof of Alexandrov's convex cap theorem
Ivan Izmestiev
We give a variational proof of the existence and uniqueness of a convex cap with the given upper boundary. The proof uses the concavity of the total scalar curvature functional on…