{
  "id": "2407.13026",
  "version": "v1",
  "published": "2024-07-17T21:28:19.000Z",
  "updated": "2024-07-17T21:28:19.000Z",
  "title": "Strichartz estimates for the Schrödinger equation on compact manifolds with nonpositive sectional curvature",
  "authors": [
    "Xiaoqi Huang",
    "Christopher D. Sogge"
  ],
  "comment": "The paper has been accepted by the Journal of Spectral Theory. arXiv admin note: substantial text overlap with arXiv:2304.05247",
  "categories": [
    "math.AP",
    "math.CA",
    "math.DG"
  ],
  "abstract": "We obtain improved Strichartz estimates for solutions of the Schr\\\"odinger equation on compact manifolds with nonpositive sectional curvatures which are related to the classical universal results of Burq, G\\'erard and Tzvetkov [11]. More explicitly, we are able refine the arguments in the recent work of Blair and the authors [3] to obtain no-loss $L^p_tL^{q}_{x}$-estimates on intervals of length $\\log \\lambda\\cdot \\lambda^{-1} $ for all {\\em admissible} pairs $(p,q)$ when the initial data have frequencies comparable to $\\lambda$, which, given the role of the Ehrenfest time, is the natural analog in this setting of the universal results in [11]. We achieve this log-gain over the universal estimates by applying the Keel-Tao theorem along with improved global kernel estimates for microlocalized operators which exploit the geometric assumptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-17T21:28:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50",
      "35P15"
    ],
    "keywords": [
      "nonpositive sectional curvature",
      "compact manifolds",
      "strichartz estimates",
      "schrödinger equation",
      "universal results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}