题目:Uniform Sobolev estimates for Laplace-Beltrami operators 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年12月1日, 周一   下午15:00-16:30

地点：管理楼1611

摘要: This talk is concerned with the uniform Sobolev estimates of the Laplace-Beltrami operator on a compact manifolds M.  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.
 
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