{
  "id": "2410.17850",
  "version": "v1",
  "published": "2024-10-23T13:19:37.000Z",
  "updated": "2024-10-23T13:19:37.000Z",
  "title": "Translating Solitons to a Lagrangian mean curvature flow with zero Maslov class",
  "authors": [
    "Xiaoli Han",
    "Jiayu Li",
    "Jun Sun"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "It is known that there is no a Type I singularity for the Lagrangian mean curvature flow with zero Maslov class. In this paper, we study translating solitons which are important models of Type II singularities. A necessary condition for a blow-up limit arising at a Type II singularity of a Lagrangian mean curvature flow with zero Maslov class is provided. As an application, we prove that the Lagrangian translating solitons constructed by Joyce-Lee-Tsui \\cite{JLT} cannot be a blow-up limit for a Lagrangian mean curvature flow with zero Maslov class, answering an open question proposed by Joyce-Lee-Tsui and Neves-Tian \\cite{NT}, as well as we also prove that the Grim Reaper cannot be a blow-up limit for a Lagrangian mean curvature flow with zero Maslov class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-23T13:19:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lagrangian mean curvature flow",
      "zero maslov class",
      "translating solitons",
      "blow-up limit",
      "singularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}