On the Multilinear Restriction and Kakeya conjectures

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We prove $d$-linear analogues of the classical restriction and Kakeya conjectures in $\R^d$. 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 $n$-linear analogues for $n<d$.
38 pages, no figures, submitted

Keywords

Classical Analysis and ODEs, 42B10

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/76319

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509262
 http://arxiv.org/abs/math/0509262

Collections

arXiv