Geodesic
The proof of the $l^2$ Decoupling Conjecture
Jean Bourgain1 ; Ciprian Demeter2
1 School of Mathematics, Einstein Drive, Institute for Advanced Study, Princeton, NJ 08540
2 Department of Mathematics, Indiana University, 831 East Third St., Bloomington, IN 47405
Annals of mathematics, Tome 182 (2015) no. 1, pp. 351-389.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove the $l^2$ Decoupling Conjecture for compact hypersurfaces with positive definite second fundamental form and also for the cone. This has a wide range of important consequences. One of them is the validity of the Discrete Restriction Conjecture, which implies the full range of expected $L^p_{x,t}$ Strichartz estimates for both the rational and (up to $N^\epsilon$ losses) the irrational torus. Another one is an improvement in the range for the discrete restriction theorem for lattice points on the sphere. Various applications to Additive Combinatorics, Incidence Geometry and Number Theory are also discussed. Our argument relies on the interplay between linear and multilinear restriction theory.
DOI : 10.4007/annals.2015.182.1.9

Jean Bourgain 1 ; Ciprian Demeter 2

1 School of Mathematics, Einstein Drive, Institute for Advanced Study, Princeton, NJ 08540
2 Department of Mathematics, Indiana University, 831 East Third St., Bloomington, IN 47405 
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Jean Bourgain; Ciprian Demeter. The proof of the $l^2$ Decoupling Conjecture. Annals of mathematics, Tome 182 (2015) no. 1, pp. 351-389. doi : 10.4007/annals.2015.182.1.9. http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.182.1.9/

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