Title: Decay of waves on conic manifolds
Abstract: The wave equation on flat space satisfies Huygens' principle (in odd spatial dimensions) and a weak Huygens' principle (in even spatial dimensions). Both the strong and weak Huygens' principles lead to non-trapping resolvent estimates and hence to asymptotic expansions for the wave equation and a local smoothing estimate for the Schrödinger equation. In this talk I will first recall the strong and weak Huygens' principles in flat space and their applications. I will then describe recent work with Jared Wunsch establishing a "very weak" Huygens' principle (and the applications of this principle) for the wave equation on a class of manifolds with conic singularities.
Tea at 4:00
Friday November 30, 2012 at 3:00 PM in SEO 636