scholarly journals Local and infinitesimal rigidity of hypersurface embeddings

2017 ◽  
Vol 369 (11) ◽  
pp. 7829-7860 ◽  
Author(s):  
Giuseppe della Sala ◽  
Bernhard Lamel ◽  
Michael Reiter
Keyword(s):  
Infinitesimal Rigidity

Infinitesimal Rigidity of Convex Polyhedra through the Second Derivative of the Hilbert–Einstein Functional

2014 ◽  
Vol 66 (4) ◽  
pp. 783-825 ◽  
Author(s):  
Ivan Izmestiev
Keyword(s):  
Existence And Uniqueness ◽  
Convex Polyhedra ◽  
Future Research ◽  
Second Derivative ◽  
De Sitter ◽  
Spherical Space ◽  
Infinitesimal Rigidity ◽  
Minkowski Theorem ◽  
Perfect Duality ◽  
Derivatives Of

Abstract. The paper presents a new proof of the infinitesimal rigidity of convex polyhedra. The proof is based on studying derivatives of the discrete Hilbert–Einstein functional on the space of “warped polyhedra” with a fixed metric on the boundary.The situation is in a sense dual to using derivatives of the volume in order to prove the Gauss infinitesimal rigidity of convex polyhedra. This latter kind of rigidity is related to the Minkowski theorem on the existence and uniqueness of a polyhedron with prescribed face normals and face areas.In the spherical space and in the hyperbolic-de Sitter space, there is a perfect duality between the Hilbert–Einstein functional and the volume, as well as between both kinds of rigidity.We review some of the related work and discuss directions for future research.

scholarly journals Infinitesimal rigidity and flexibility of a non-symmetric affine connection space

2010 ◽  
Vol 31 (4) ◽  
pp. 1148-1159 ◽  
Author(s):  
Ljubica S. Velimirović ◽  
Svetislav M. Minčić ◽  
Mića S. Stanković
Keyword(s):  
Affine Connection ◽  
Infinitesimal Rigidity ◽  
Connection Space

scholarly journals On the infinitesimal rigidity of weakly convex polyhedra

2010 ◽  
Vol 31 (4) ◽  
pp. 1080-1090 ◽  
Author(s):  
Robert Connelly ◽  
Jean-Marc Schlenker
Keyword(s):  
Convex Polyhedra ◽  
Infinitesimal Rigidity ◽  
Weakly Convex
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