Mathematical Sciences: Extremal Sobolev Inequalities and Applications

首席研究员将继续研究 上的极值函数和极值Sobolev不等式 傅立叶分析中的问题，非线性部分 微分方程和频谱分析。 过去三 多年来，她应用索伯列夫不等式的问题， 在2-球面上规定高斯曲率， n-球面上的曲率与紧空间上的等谱问题 流形 在这个项目中，首席研究员将研究 以下四个问题使用极值Sobolev不等式： Szego投影定理，对数行列式公式 对于n-球面上的共形拉普拉斯算子，进一步的工作 紧的规定曲率和一致化定理 二维流形

The principal investigator will continue her study of extremal functions and extremal Sobolev inequalities in the context of problems in Fourier analysis, nonlinear partial differential equations and spectral analysis. In the past three years she has applied Sobolev inequalities to problems involving prescribing the Gaussian curvature on the 2-sphere and the scalar curvature on the n-sphere and to isospectral problems on compact manifolds. In this project the principal investigator will study the following four problems using extremal Sobolev inequalities: Szego's projection theorem, the logarithm determinant formula for the conformal Laplacian on the n-sphere, further work on prescribing curvature and the Uniformization Theorem for compact 2-manifolds.