New proofs are given for Cauchy's and Alexandrov's classical theorem
on the rigidity of polyhedral frameworks, as well as their higher
dimensional generalizations. Through duality, the rigidity of these
frameworks follows from characterizations of the case of equality
in Minkowski's quadratic inequality.
*52C25 Rigidity and flexibility of structures 52B11 n-dimensional
polytopes 52B05 Combinatorial properties of convex sets 52A39 Mixed
volumes and related topics (convex geometry)
%0 Journal Article
%1 765.52017
%A Filliman, P.
%D 1992
%J Monatsh. Math.
%K $g$-theorem; Cauchy's Maxwell-Cremona Theorem; duality} frameworks; inequality; mixed of polyhedral rigidity stress; volumes; {Alexandrov-Fenchel
%N 1
%P 1-22
%T Rigidity and the Alexandrov-Fenchel inequality.
%V 113
%X New proofs are given for Cauchy's and Alexandrov's classical theorem
on the rigidity of polyhedral frameworks, as well as their higher
dimensional generalizations. Through duality, the rigidity of these
frameworks follows from characterizations of the case of equality
in Minkowski's quadratic inequality.
@article{765.52017,
abstract = {{New proofs are given for Cauchy's and Alexandrov's classical theorem
on the rigidity of polyhedral frameworks, as well as their higher
dimensional generalizations. Through duality, the rigidity of these
frameworks follows from characterizations of the case of equality
in Minkowski's quadratic inequality.} },
added-at = {2008-03-02T02:12:02.000+0100},
author = {Filliman, P.},
biburl = {https://www.bibsonomy.org/bibtex/26ccae09893786be383664ba3920c8ab0/dmartins},
classmath = {{*52C25 Rigidity and flexibility of structures 52B11 n-dimensional
polytopes 52B05 Combinatorial properties of convex sets 52A39 Mixed
volumes and related topics (convex geometry)}},
description = {robotica-bib},
interhash = {1b77082021ced0d1c19c350b9a33392d},
intrahash = {6ccae09893786be383664ba3920c8ab0},
journal = {Monatsh. Math.},
keywords = {$g$-theorem; Cauchy's Maxwell-Cremona Theorem; duality} frameworks; inequality; mixed of polyhedral rigidity stress; volumes; {Alexandrov-Fenchel},
language = {English},
number = 1,
pages = {1-22},
reviewer = {{P.Filliman}},
timestamp = {2008-03-02T02:12:50.000+0100},
title = {{Rigidity and the Alexandrov-Fenchel inequality.}},
volume = 113,
year = 1992
}