Flat tori in three-dimensional space and convex integration.

  title={Flat tori in three-dimensional space and convex integration.},
  author={Vincent Borrelli and Sa{\"i}d Jabrane and Francis Lazarus and Boris Thibert},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  volume={109 19},
It is well-known that the curvature tensor is an isometric invariant of C(2) Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity C(1). This unexpected flexibility has many paradoxical consequences, one of them is the existence of C(1) isometric embeddings of flat tori into Euclidean three-dimensional space. In the 1970s and… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 12 references

Introduction to the h-principle (Graduate Studies in Mathematics, vol

Y Eliashberg, N Mishachev
View 14 Excerpts
Highly Influenced

Encounter with a Geometer , Part II

View 6 Excerpts
Highly Influenced

Partial Differential Relations (Springer, Berlin

M Gromov
View 4 Excerpts
Highly Influenced

C1-isometric imbeddings

J Nash
Annals of Mathematics • 1954
View 15 Excerpts
Highly Influenced

h-Principle and Flexibility in Geometry

H Geiges
(Mem. of the A.M.S, • 2003
View 10 Excerpts
Highly Influenced

On C1-isometric imbeddings

N Kuiper
Indag. Math. 17:545-556 • 1955
View 6 Excerpts
Highly Influenced

Le paradoxe de Scheffer-Shnirelman revu sous l’angle de l’intégration convexe

C Villani
Séminaire Bourbaki, • 2010
View 1 Excerpt

The shape of a long leaf.

Proceedings of the National Academy of Sciences of the United States of America • 2009
View 1 Excerpt

The intrinsic geometry of the cerebral cortex.

Journal of theoretical biology • 1994
View 1 Excerpt

Similar Papers

Loading similar papers…