The Nash-Kuiper process for curves

Vincent Borrelli (1) , Saïd Jabrane (1) , Francis Lazarus (2) , Boris Thibert (3)

1 ICJ - Institut Camille Jordan
2 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes
3 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

A strictly short embedding is an embedding of a Riemannian manifold into an Euclidean space that strictly shortens distances. From such an embedding, the Nash-Kuiper process builds a sequence of maps converging toward an isometric embedding. In that paper, we describe this Nash-Kuiper process in the case of curves. We state an explicit formula for the limit normal map and perform its Fourier series expansion. We then address the question of Holder regularity of the limit map.

Domaines: Géométrie algorithmique [cs.CG]

Vincent Borrelli, Saïd Jabrane, Francis Lazarus, Boris Thibert. The Nash-Kuiper process for curves. Séminaire de Théorie Spectrale et Géométrie, 2012, 30, pp.1-19. ⟨10.5802/tsg.288⟩. ⟨hal-00864494⟩