{
  "id": "2009.12895",
  "version": "v1",
  "published": "2020-09-27T16:48:20.000Z",
  "updated": "2020-09-27T16:48:20.000Z",
  "title": "The Semiclassical Resolvent on Conic Manifolds and Application to Schrödinger Equations",
  "authors": [
    "Xi Chen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article, we shall construct the resolvent of Laplacian at high energies near the spectrum on non-product conic manifolds with a single cone tip. Microlocally, the resolvent kernel is the sum of b-pseudodifferential operators, scattering pseudodifferential operators and intersecting Legendrian distributions. As an application, we shall establish Strichartz estimates for Schr\\\"odinger equations on non-compact manifolds with multiple non-product conic singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-27T16:48:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger equations",
      "semiclassical resolvent",
      "application",
      "multiple non-product conic singularities",
      "non-product conic manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}