Journal of Differential Geometry

Volume increasing isometric deformations of convex polyhedra

David D. Bleecker

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 43, Number 3 (1996), 505-526.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214458323

Digital Object Identifier
doi:10.4310/jdg/1214458323

Mathematical Reviews number (MathSciNet)
MR1412676

Zentralblatt MATH identifier
0864.52003

Subjects
Primary: 52B60: Isoperimetric problems for polytopes
Secondary: 52B10: Three-dimensional polytopes

Citation

Bleecker, David D. Volume increasing isometric deformations of convex polyhedra. J. Differential Geom. 43 (1996), no. 3, 505--526. doi:10.4310/jdg/1214458323. https://projecteuclid.org/euclid.jdg/1214458323


Export citation

References

  • [1] A. D. Aleksandrov, Konvexe polyeder, Akademic - Verlag, Berlin, 1958.
  • [2] A. D. Aleksandrov and V. A. Zalgaller, Intrinsic geometry of surfaces, (Transl. Math. Monographs, Vol. 15) Providence, RI, Amer. Math. Soc, 1967.
  • [3] M. Berger, Geometry II, Springer, Berlin, 1987.
  • [4] D. D. Bleecker, Isometric deformations of compact hypersurfaces, Geom. Dedicata, to appear.
  • [5] Y. D. Burago and V. A. Zalgaller, Polyhedral embedding of a net, Vestnik Leningrad. Univ. 15 (1960) 66-80.
  • [6] H. Busemann, Convex surfaces, Interscience, New York, 1958.
  • [7] A. Cauchy, Sur les polygones et polyedres, 2nd Mem. J. Ecole Polytechn. 9 (1813) 87.
  • [8] R. Connelly, Conjectures and open questions in rigidity, Proc. Internat. Congr. Math. (Helsinki, 1978), Acad. Sci., Fennica, Helsinki, 1980.
  • [9] H. S. M. Coxeter, Regular complex polytopes, Cambridge University Press, Cambridge, 1991.
  • [10] N. V. Efimov, Qualitative problems in the theory of deformations of surfaces, Differential Geometry and Calculus of Variations, 274-423, Transl., Ser. 1, Vol. 6, Amer. Math. Soc, Providence, RI, 1962.
  • [11] B. Grunbaum, Convex polytopes, Interscience, New York, 1967.
  • [12] N. H. Kuiper, On C1 isometric imbeddings I, Indag. Math. 17 (1955) 545-556.
  • [13] L. A. Lyusternik, Convex figures and polyhedra, Heath, Boston, 1966.
  • [14] W. H. Paulsen, What is the shape of a mylar balloon?, Amer. Math. Monthly 101 (1994) 953-958.
  • [15] A. V. Pogorelov, Extrinsic geometry of convex surfaces, (Translations of Mathematical Monographs, Vol. 35) Amer. Math. Soc, Providence, RI, 1973.