Degree reduction and graininess for Kakeya-type sets in R3

• Larry Guth ^[1]
  1. [1] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 2, 2016, págs. 447-494
• Idioma: inglés
• DOI: 10.4171/RMI/891
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let T be a set of cylindrical tubes in R3 of length N and radius 1. If the union of the tubes has volume N3−σ, and each point in the union lies in tubes pointing in three quantitatively different directions, and if a technical assumption holds, then at scale Nσ, the tubes are clustered into rectangular slabs of dimension 1×Nσ×Nσ. This estimate generalizes the graininess estimate in [7]. The proof is based on modeling the union of tubes with a high-degree polynomial.