{
  "id": "2101.06024",
  "version": "v1",
  "published": "2021-01-15T09:20:51.000Z",
  "updated": "2021-01-15T09:20:51.000Z",
  "title": "A probabilistic representation for heat flow of harmonic map on manifolds with time-dependent Riemannian metric",
  "authors": [
    "Xin Chen",
    "Wenjie Ye"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we will give a probabilistic representation for the heat flow of harmonic map with time-dependent Riemannian metric via a forward-backward stochastic differential equation on manifolds. Moreover, we can provide an alternative stochastic method for the proof of existence of a unique local solution for heat flow of harmonic map with time-dependent Riemannian metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-15T09:20:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time-dependent riemannian metric",
      "heat flow",
      "harmonic map",
      "probabilistic representation",
      "unique local solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}