29,291 research outputs found
Counting joints in vector spaces over arbitrary fields
We give a proof of the "folklore" theorem that the
Kaplan--Sharir--Shustin/Quilodr\'an result on counting joints associated to a
family of lines holds in vector spaces over arbitrary fields, not just the
reals. We also discuss a distributional estimate on the multiplicities of the
joints in the case that the family of lines is sufficiently generic.Comment: Not intended for publication. References added and other minor edits
in this versio
On the Dimension of Finite Point Sets I. An Improved Incidence Bound for Proper 3D sets
We improve the well-known Szemer\'edi-Trotter incidence bound for proper
3--dimensional point sets (defined appropriately)Comment: Unpublished manuscript from the late Gyuri Elekes. It was edited on
2007.04.27. last tim
On the Multilinear Restriction and Kakeya conjectures
We prove -linear analogues of the classical restriction and Kakeya
conjectures in . Our approach involves obtaining monotonicity formulae
pertaining to a certain evolution of families of gaussians, closely related to
heat flow. We conclude by giving some applications to the corresponding
variable-coefficient problems and the so-called "joints" problem, as well as
presenting some -linear analogues for .Comment: 38 pages, no figures, submitte
- …