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Session S33 - Spectral Geometry

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Uniform Sobolev estimates on compact manifolds involving singular potentials.

Xiaoqi Huang

Johns Hopkins University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We will discuss generalizations of the uniform Sobolev inequalities of Kenig, Ruiz and Sogge for Euclidean spaces and Dos Santos Ferreira, Kenig and Salo for compact Riemannian manifolds involving critically singular potentials V ∈ Ln/2. We shall also discuss the analogous improved quasimode estimates as well as analogues of the improved uniform Sobolev estimates involving such potentials under certain geometric conditions.

Joint work with Matthew D. Blair (University of New Mexico), Yannick Sire (Johns Hopkins University) and Christopher Sogge (Johns Hopkins University).

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