Advances in Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
Main page
About this project
Software
Classifications
Links
Terms of Use

Search papers
Search references

RSS
Current issues
Archive issues
What is RSS






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Adv. Math., 2014, Volume 252, Pages 586–611 (Mi admat8)  

Sabitov polynomials for volumes of polyhedra in four dimensions

A. A. Gaifullinab

a Institute for Information Transmission Problems, Bolshoy Karetny per. 19, Moscow, 127994, Russia
b Steklov Mathematical Institute, Gubkina str. 8, Moscow, 119991, Russia

Abstract: In 1996 I.Kh. Sabitov proved that the volume of a simplicial polyhedron in a 3-dimensional Euclidean space is a root of certain monic polynomial with coefficients depending on the combinatorial type and on edge lengths of the polyhedron only. Moreover, the coefficients of this polynomial are polynomials in edge lengths of the polyhedron. This result implies that the volume of a simplicial polyhedron with fixed combinatorial type and edge lengths can take only finitely many values. In particular, this yields that the volume of a flexible polyhedron in a 3-dimensional Euclidean space is constant. Until now it has been unknown whether these results can be obtained in dimensions greater than 3. In this paper we prove that all these results hold for polyhedra in a 4-dimensional Euclidean space.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-92102
11-01-00694
Ministry of Education and Science of the Russian Federation 11.G34.31.0005
Dynasty Foundation
Russian Academy of Sciences - Federal Agency for Scientific Organizations
The work was partially supported by the Russian Foundation for Basic Research (projects 10-01-92102 and 11-01-00694), by a grant of the Government of the Russian Federation (project 11.G34.31.0005), by a grant from Dmitri Ziminʼs “Dynasty” foundation and by a programme of the Branch of Mathematical Sciences of the Russian Academy of Sciences.


DOI: https://doi.org/10.1016/j.aim.2013.11.005


Bibliographic databases:

MSC: 51M25, 52B11, 13P15
Received: 22.10.2011
Accepted:18.11.2013
Language:

Linking options:
  • http://mi.mathnet.ru/eng/admat8

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:94

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021