Hevea Project :

h-principle, visualization and applications

Convex integration is a mathematical theory developed by Mikhaïl Gromov in order to solve partial differential equations. This theory shows that a property, called h-principle, is satisfied by many equations.

The Hévéa Project aims at showing that Convex integration provides an effective tool to build explicit solutions of fundamental geometric equations. Based on this effective tool, the Hévéa team has achieved in 2012 the first visualization of an isometric embedding of a flat torus.


Galleries



and the YouTube channel of the Hevea Project!



3D print / Code




Outreach folder




The hyperbolic plane / Research article

2023
The Hyperbolic Plane in E3
by V. Borrelli, R. Denis, F. Lazarus, M. Theillière, B. Thibert

Ph.D. theses related to the Hevea project

2019
Polyhedral embeddings of the Flats Square Torus
by Tanessi Quintanar Cortés

2019
Effective Convex Integration
by M. Theillière

Reduced sphere / Research article

2018
An explicit isometric reduction of the unit sphere into an arbitrarily small ball
by E. Bartzos, V. Borrelli, R. Denis, F. Lazarus, D. Rohmer, B. Thibert

Flat torus / Research articles

2013
Isometric embeddings of the square flat torus in ambient space
by V. Borrelli, S. Jabrane, F. Lazarus, B. Thibert

2012
Flat tori in three-dimensional space and convex integration
by V. Borrelli, S. Jabrane, F. Lazarus, B. Thibert

Flat torus / Other texts

2011
Mini-cours à Nantes (mars 2011)
by Vincent Borrelli
Leçon 1 Leçon 2 Leçon 3

2011
Groupe de travail TOPIC (TOres Plats et Integration Convexe)
by Hevea team and Cédric Villani
Topic 1 Topic 2 Topic 3 Topic 4

2011
The Nash-Kuiper process for curves
by V. Borrelli, S. Jabrane, F. Lazarus, B. Thibert

2009
Le h-principe ? (Gazette des Maths, octobre 2009)
by V. Borrelli


Our works in other Media


See the dedicated webpage.



Team


Former members


  • Saïd Jabrane

  • Ancien doctorant à l'ICJ, Lyon 1


  • Tanessi Quintanar

  • Ancienne doctorante à l'ICJ, Lyon 1


Website designed by Mélanie Theillière