On metric cones, multiplicity of conjugate points within distance π on the boundary causes |t|^{1/2} loss in long-time decay and half-order regularity shift for Schrödinger dispersive estimates, except when the Legendre submanifold satisfies a proposed admissible condition.
Propagation of singularities and Fredholm analysis of the time-dependent Schr¨ odinger equation.arXiv preprint arXiv:2201.03140, 2022
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The effect of geometric focusing on dispersive estimates for Schr\"odinger and wave equations
On metric cones, multiplicity of conjugate points within distance π on the boundary causes |t|^{1/2} loss in long-time decay and half-order regularity shift for Schrödinger dispersive estimates, except when the Legendre submanifold satisfies a proposed admissible condition.