Reference : Holonomic approximation through convex integration
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Physical, chemical, mathematical & earth Sciences : Mathematics
Holonomic approximation through convex integration
Massot, Patrick mailto [Université Paris-Sud 11 > Laboratoire de Mathématiques d'Orsay]
Theilliere, Mélanie mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
[en] h-principle
[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.
ANR ; Fonds National de la Recherche - FnR
ANR/FNR project SoS
FnR ; FNR11554412 > Hugo Parlier > SoS > Structures On Surfaces > 01/04/2018 > 30/09/2022 > 2016

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