Abstract
We build polyhedral complexes in R that coincide with dyadic grids with different orientations, while keeping uniform lower bounds (depending only on n) on the flatness of the added polyhedrons including their subfaces in all dimensions. After the definitions and first properties of compact Euclidean polyhedrons and complexes, we introduce a tool allowing us to fill with n-dimensionnal polyhedrons a tubular-shaped open set, the boundary of which is a given n − 1-dimensionnal complex. The main result is proven inductively over n by completing our dyadic grids layer after layer, filling the tube surrounding each layer and using the result in the previous dimension to build the missing parts of the tube boundary. A possible application of this result is a way to find solutions to problems of measure minimization over certain topological classes of sets, in arbitrary dimension and codimension.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Bulletin de la Société mathématique de France
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
