$L^p$ estimates for eigenfunctions on manifolds with boundary

Date & time

1.30–2.30pm 21 March 2017


John Dedman Building 27, Room G35


Melissa Tacy (ANU)


 Qirui Li

Measuring the $L^p$ mass of an eigenfunction allows us to determine its concentration properties. On a manifold without boundary such estimates follow from short time properties of the wave or semiclassical Schr\"odinger propagators. However the presence of a boundary opens the possibility for multiple reflections even in short time. This will lead to greater concentration of the eigenfunction (displayed by higher $L^p$ norms). It is known, for example, that the whispering gallery modes show this higher concentration. In this talk I will discuss the whispering gallery modes from a semiclassical perspective and introduce a method for studying such eigenfunctions semiclassically on general manifolds.


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