Gauss rigidity and volume preservation under preserving curvature deformations for hedgehogs

DOI10.1007/s00025-012-0248-8zbMath1280.53003OpenAlexW1992925874MaRDI QIDQ351095

Yves Martinez-Maure

Publication date: 11 July 2013

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-012-0248-8

zbMATH Keywords

Minkowski problemalgebraic volumeGauss infinitesimal rigidityGauss rigidityhedgehogs

Mathematics Subject Classification ID

Rigidity results (53C24) Surfaces in Euclidean and related spaces (53A05) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Minkowski geometries in nonlinear incidence geometry (51B20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniqueness results for the Minkowski problem extended to hedgehogs
• New notion of index for hedgehogs of \(\mathbb R^3\) and applications
• A counterexample to the rigidity conjecture for polyhedra
• New geometric inequalities for hedgehogs
• The Bellows conjecture
• Rigidity and flexibility of virtual polytopes
• Rigidity of certain polyhedra in \(\mathbf R^3\)
• On a conjectured characterization of the sphere
• Infinitesimal rigidity of smooth convex surfaces through the second derivative of the Hilbert–Einstein functional
• Geometric Study of Minkowski Differences of Plane Convex Bodies
• The Weyl and Minkowski problems in differential geometry in the large
• Hedgehogs and zonoids