余维数大于1的曲面的双线性约束估计
Bilinear restriction estimates for surfaces of codimension bigger than one
摘要：
关于$\mathbb R^n$中对球面和抛物面等超曲面的约束问题，双线性（伴随）约束估计得到了广泛的研究。然而，没有太多的是已知的，这样的估计与余维（和尺寸）大于一个表面。在本文中，我们证明了尖锐的双线性$L^2 \times L^2 \to L^q$限制估计一般曲面的高余维。在某些特殊情况下，我们可以应用这些结果得到相应的线性估计。
英文摘要：
In connection with the restriction problem in $\mathbb R^n$ for hypersurfaces including the sphere and paraboloid, the bilinear (adjoint) restriction estimates have been extensively studied. However, not much is known about such estimates for surfaces with codimension (and dimension) larger than one. In this paper we show sharp bilinear $L^2 \times L^2 \to L^q$ restriction estimates for general surfaces of higher codimension. In some special cases, we can apply these results to obtain the corresponding linear estimates.
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