Remplissage De L'Espace Euclidien Par Des Complexes Poly\'Edriques D'Orientation Impos\'Ee Et De Rotondit\'E Uniforme

摘要

We build polyhedral complexes in Rn that coincide with dyadic grids withdifferent orientations, while keeping uniform lower bounds (depending only onn) on the flatness of the added polyhedrons including their subfaces in alldimensions. After the definitions and first properties of compact Euclideanpolyhedrons and complexes, we introduce a tool allowing us to fill withn-dimensionnal polyhedrons a tubular-shaped open set, the boundary of which isa given n - 1-dimensionnal complex. The main result is proven inductively overn by completing our dyadic grids layer after layer, filling the tubesurrounding each layer and using the result in the previous dimension to buildthe missing parts of the tube boundary. A possible application of this resultis a way to find solutions to problems of measure minimization over certaintopological classes of sets, in arbitrary dimension and codimension.