Contributors: Institute of Science and Technology Klosterneuburg, Austria (IST Austria); Sans affiliation; Université Côte d'Azur (UniCA); Understanding the Shape of Data (DATASHAPE); Centre Inria d'Université Côte d'Azur; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO); Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de l'Université Paris-Saclay; Centre Inria de Saclay; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre Inria de Saclay; Institut National de Recherche en Informatique et en Automatique (Inria); Funding This research has been supported by the European Research Council (ERC), grant No.788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31, and bythe DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant No. I02979-N35.Mathijs Wintraecken: Supported by the European Union’s Horizon 2020 research and innovationprogramme under the Marie Skłodowska-Curie grant agreement No. 754411, the Austrian sciencefund (FWF) grant No. M-3073, and the welcome package from IDEX of the Université Côte d’Azur.; Wolfgang Mulzer; Jeff M. Phillips; European Project: 788183,ERC-2017-ADG,ERC-2017-ADG,ALPHA(2018); European Project: 754411,H2020-MSCA-COFUND-2016,H2020-MSCA-COFUND-2016,ISTplus(2017)
نبذة مختصرة : This is the conference version the full version can be found at: hal-04297370 ; International audience ; We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let S ⊆ Rdbe a fixed closed set that contains a bounding sphere. That is, the bounding sphere is part of theset S. Consider the space of C1,1 diffeomorphisms of Rd to itself, which keep the bounding sphereinvariant. The map from this space of diffeomorphisms (endowed with a Banach norm) to the spaceof closed subsets of Rd (endowed with the Hausdorff distance), mapping a diffeomorphism F to theclosure of the medial axis of F (S), is Lipschitz. This extends a previous stability result of Chazaland Soufflet on the stability of the medial axis of C2 manifolds under C2 ambient diffeomorphisms.
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