119 citations · 463 across the 37 of their papers we have counts for
8 papers · 1 filter
Global regularity of wave maps I. Small critical Sobolev norm in high dimension
Terence Tao
We show that wave maps from Minkowski space to a sphere are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space …
Some light on Littlewood-Paley theory
Michael Cowling, Terence Tao
The purpose of this note is to correct an error in a paper of M. Cowling, G. Fendler and J.J.F. Fournier, and to give a counterexample to a conjecture of J.-L. Rubio de Francia.
Recent progress on the Kakeya conjecture
Nets Katz, Terence Tao
The purpose of this article is to survey the developments on the Kakeya problem in recent years, concentrating on the period after the excellent 1999 survey of Wolff, and including…
From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE
Terence Tao
We survey the interconnections between geometric combinatorics (such as the Kakeya problem), arithmetic combinatorics (such as the classical problem of determining which sets conta…
Multilinear weighted convolution of functions, and applications to non-linear dispersive equations
Terence Tao
The spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behaviour of non-linear disper…
An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension
Izabella Laba, Terence Tao
We use geometrical combinatorics arguments, including the ``hairbrush'' and x-ray arguments of Wolff and the sticky/plany/grainy analysis of Katz, Laba, and Tao, to show that Besic…