Uniform Sobolev estimates for the Laplacian on compact manifolds
主 题: Uniform Sobolev estimates for the Laplacian on compact manifolds
报告人: 尧小华 (华中师范大学数学与统计学院)
时 间: 2014-12-17 10:30-11:30
地 点: 理科一号楼1479（主持人：郭紫华）
This talk is concerned with the uniform Sobolev estimates of the Laplace-Beltrami operator on a compact manifolds. Specifically, if the pair (1/p, 1/q) is on the Sobolev line 1/p?1/q=2/n and p<2(n+1)/(n+3) and q>2(n+1)/(n?1), then we will prove that the resolvent is uniformly Lp-Lq-bounded outside a parabola opening to the right and a small disk centered at the origin, which is optimal on Sphere (or Zoll manifolds). Using the shrinking spectral project estimates, we further obtain a Logarithmic improvement over the parabolic region for resolvent estimates on manifolds with non-positive sectional curvature and a power improvement for flat torus. The main results are closely associated with spectral theory on manifolds and oscillatory integral of harmonic analysis.
