Details

Autor(en) / Beteiligte

• Baskin, Dean
• Wunsch, Jared

Titel

Resolvent estimates and local decay of waves on conic manifolds

Ist Teil von

• Journal of differential geometry, 2013-10, Vol.95 (2), p.183-214

Ort / Verlag

Lehigh University

Erscheinungsjahr

2013

Link zum Volltext

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• We consider manifolds with conic singularities that are isometric to \mathbb{R}^n outside a compact set. Under natural geometric assumptions on the cone points, we prove the existence of a logarithmic resonance-free region for the cut-off resolvent. The estimate also applies to the exterior domains of non-trapping polygons via a doubling process. ¶ The proof of the resolvent estimate relies on the propagation of singularities theorems of Melrose and the second author to establish a “very weak” Huygens’ principle, which may be of independent interest. ¶ As applications of the estimate, we obtain a exponential local energy decay and a resonance wave expansion in odd dimensions, as well as a lossless local smoothing estimate for the Schrödinger equation.