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Diffractive propagation on conic manifolds. (English) Zbl 1360.58017

In the interesting survey under review, the author presents some applications and extensions of the joint results with Richard Melrose regarding propagation of singularities for solutions to the wave equation on manifolds with conical singularities.
The results given mainly concern:
The local decay of energy on noncompact manifolds with diffractive trapped orbits [D. Baskin and J. Wunsch, J. Differ. Geom. 95, No. 2, 183–214 (2013; Zbl 1296.53075)];
Singularities of the wave trace created by diffractive closed geodesics [G. A. Ford and J. Wunsch, Adv. Math. 304, 1330–1385 (2017; Zbl 1378.53050)];
The distribution of scattering resonances associated to such closed geodesics (joint work with Luc Hillairet).

MSC:

58J05 Elliptic equations on manifolds, general theory
58J45 Hyperbolic equations on manifolds
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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References:

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