2 Rigidity and volume preserving deformation in R n 2

@inproceedings{Zhang20072RA,
  title={2 Rigidity and volume preserving deformation in R n 2},
  author={Lizhao Zhang},
  year={2007}
}
Given a degenerate (n+1)-simplex in a n-dimensional Euclidean space Rn and a k with 1 ≤ k ≤ n, we separate all its k-faces into 2 groups by following certain rules. We allow all its vertices to have continuous motion in Rn while giving the following restriction: the volume of the k-faces in the 1st group can not increase (these faces are called “k-cables”), and the volume of the k-faces in the 2nd group can not decrease (“k-struts”). Assuming some smoothness property, we prove that all the… CONTINUE READING

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-9 of 9 references

Two-distance preserving functions from Euclidean space

  • K. Bezdek, R. Connelly
  • Discrete geometry and rigidity(Budapest, 1999…
  • 1999
Highly Influential
5 Excerpts

Rigidity

  • R. Connelly
  • in: Handbook of convex geometry, Vol. A…
  • 1993
Highly Influential
5 Excerpts

Rigidity and Invariance Properties of Certain Geometric Frameworks

  • L. Zhang
  • PhD Thesis, MIT
  • 2002
1 Excerpt

The bellows conjecture

  • R. Connelly, I. Sabitov, A. Walz
  • Contributions to Algebra and Geometry, 38
  • 1997
1 Excerpt

On the problem of invariance of the volume of a flexible polyhedron

  • I. Sabitov
  • Russian Mathematical Surveys, 50
  • 1995
2 Excerpts

The Schläfli differential equality

  • J. Milnor
  • Collected papers, Vol. 1, Publish or Perish
  • 1994
1 Excerpt

Elementary Geometry in Hyperbolic Space

  • W. Fenchel
  • Berlin; New York: W. de Gruyter
  • 1989
1 Excerpt

Mémoire sur les fonctions alternées et sur les sommes alternées

  • A. L. Cauchy
  • Exercices Anal. et Phys. Math. 2
  • 1841
2 Excerpts

Similar Papers

Loading similar papers…