{
  "id": "2201.09466",
  "version": "v1",
  "published": "2022-01-24T05:37:44.000Z",
  "updated": "2022-01-24T05:37:44.000Z",
  "title": "Propagation of singularities under Schrödinger equations on manifolds with ends",
  "authors": [
    "Shota Fukushima"
  ],
  "comment": "47 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a microlocal smoothing effect of Schr\\\"odinger equations on manifolds. We employ radially homogeneous wavefront sets introduced by Ito and Nakamura (Amer. J. Math., 2009). In terms of radially homogeneous wavefront sets, we can apply our theory to both of asymptotically conical and hyperbolic manifolds. We relate wavefront sets in initial states to radially homogeneous wavefront sets in states after a time development. We also prove a relation between radially homogeneous wavefront sets and homogeneous wavefront sets and prove a special case of Nakamura (2005).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-24T05:37:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger equations",
      "singularities",
      "propagation",
      "employ radially homogeneous wavefront sets",
      "relate wavefront sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}