Affine-invariant Fourier Restriction for general varieties

仿射不变调和分析作为一种强有力的观点出现，它统一并使许多先前的结果更加自动化，这些结果依赖于底层变化的曲率简并。最近，建立l2傅里叶限制估计的经典Stein-Tomas论证被修改为对从曲线到超曲面的任意指定维数的一类变异给出尖锐估计。在这个项目中，我们提出了一个l2仿射不变傅里叶限制理论

Affine-invariant harmonic analysis has emerged as a powerful perspective, unify-ing and making more robost many previous results which depended on curvaturedegeneracy of the underlying variety.Recemtly the classical Stein-Tomas argument establishing L 2 fourier restrictionestimates have been modified to give sharp estimates for a class of varieties with anyprescribed dimension, from curves to hypersurfaces. In this project, it is proposedthat an L 2 affine-invariant fourier restriction theory be developed for this class ofvarieties