A proof of the Farkas-Minkowski theorem by a tandem method

2017 ◽  
Vol 69 (1) ◽  
pp. 142-150
Author(s):  
Takao Fujimoto ◽  
B. B. Upeksha P. Perera ◽  
Giorgio Giorgi
Keyword(s):  
Minkowski Theorem

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 On the equality conditions of the Brunn-Minkowski theorem

2011 ◽  
Vol 139 (10) ◽  
pp. 3719-3719 ◽  
Author(s):  
Daniel A. Klain
Keyword(s):  
Minkowski Theorem

A Nonsymmetric Hasse-Minkowski Theorem

1977 ◽  
Vol 99 (4) ◽  
pp. 755 ◽  
Author(s):  
William C. Waterhouse
Keyword(s):  
Minkowski Theorem

scholarly journals Expanding translates of curves and Dirichlet-Minkowski theorem on linear forms

2009 ◽  
Vol 23 (2) ◽  
pp. 563-589 ◽  
Author(s):  
Nimish A. Shah
Keyword(s):  
Linear Forms ◽  
Minkowski Theorem

A Minkowski Theorem (Optional)

2000 ◽  
pp. 129-138
Keyword(s):  
Minkowski Theorem

Random minkowski theorem

2011 ◽  
Vol 47 (4) ◽  
pp. 398-402
Author(s):  
G. A. Margulis
Keyword(s):  
Minkowski Theorem

scholarly journals ANNIHILATING IDEALS OF QUADRATIC FORMS OVER LOCAL AND GLOBAL FIELDS

2010 ◽  
Vol 06 (03) ◽  
pp. 603-624
Author(s):  
KLAAS-TIDO RÜHL
Keyword(s):  
Quadratic Form ◽  
Equivalence Class ◽  
Local Field ◽  
Quadratic Forms ◽  
Global Field ◽  
Witt Rings ◽  
Global Fields ◽  
Minkowski Theorem ◽  
Isometry Class

We study annihilating polynomials and annihilating ideals for elements of Witt rings for groups of exponent 2. With the help of these results and certain calculations involving the Clifford invariant, we are able to give full sets of generators for the annihilating ideal of both the isometry class and the equivalence class of an arbitrary quadratic form over a local field. By applying the Hasse–Minkowski theorem, we can then achieve the same for an arbitrary quadratic form over a global field.

scholarly journals The Minkowski theorem for max-plus convex sets

2007 ◽  
Vol 421 (2-3) ◽  
pp. 356-369 ◽  
Author(s):  
Stéphane Gaubert ◽  
Ricardo D. Katz
Keyword(s):  
Convex Sets ◽  
Minkowski Theorem
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