Speaker: Xiaoqi Huang (University of Maryland)
Venue: Tencent meeting ID: 242 153 274
Abstract：In this talk we will discuss improved spectral cluster and Weyl reminder estimates on certain product manifolds. In particular, if we assume that Y is a compact Riemannian manifold with improved Lq eigenfunction estimates then, at least for large enough exponents, one always obtains improved Lq bounds on the product manifold X×Y if X is another compact manifold. Similarly, improved Weyl remainder term bounds on the spectral counting function of Y lead to corresponding improvements on X×Y. The proof is based on the structure of the product metric and the kernel estimates for Bochner-Riesz operators on compact manifold. This is based on joint work with Christopher Sogge and Micheal Taylor.