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Holonomic approximation through convex integration
Massot, Patrick; THEILLIERE, Mélanie
2021
 

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Keywords :
h-principle
Abstract :
[en] Convex integration and the holonomic approximation theorem are two well-known pillars of flexibility in differential topology and geometry. They may each seem to have their own flavor and scope. The goal of this paper is to bring some new perspective on this topic. We explain how to prove the holonomic approximation theorem for first order jets using convex integration. More precisely we first prove that this theorem can easily be reduced to proving flexibility of some specific relation. Then we prove this relation is open and ample, hence its flexibility follows from off-the-shelf convex integration.
Disciplines :
Mathematics
Author, co-author :
Massot, Patrick;  Université Paris-Sud 11 > Laboratoire de Mathématiques d'Orsay
THEILLIERE, Mélanie ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Language :
English
Title :
Holonomic approximation through convex integration
Publication date :
09 July 2021
Number of pages :
11
FnR Project :
FNR11554412 - Structures On Surfaces, 2016 (01/04/2018-30/09/2022) - Hugo Parlier
Name of the research project :
ANR/FNR project SoS
Funders :
ANR - Agence Nationale de la Recherche [FR]
FNR - Fonds National de la Recherche [LU]
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since 21 October 2021

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