The proof of the l2 Decoupling Conjecture
The proof of the l2 Decoupling Conjecture
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DOI：
10.4007/annals.2015.182.1.9
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发表时间：
2015-07-01
影响因子：
4.9
通讯作者：
Demeter, Ciprian
中科院分区：
文献类型：
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作者：
Bourgain, Jean;Demeter, Ciprian
证明了L(2)关于具有正定第二基本形式的紧致超曲面和锥面的解耦猜想。这产生了广泛的重要后果。其中之一是离散限制猜想的有效性，它暗示了有理环面和(直到N-epsilon损失)无理环面的L-x，t(P)Strichartz估计的全部预期范围。另一个是对球面上格点离散限制定理的范围的改进。文中还讨论了加性组合数学、关联几何和数论的各种应用。我们的论点依赖于线性和多线性限制理论之间的相互作用。
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-x,t(p) 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.