{
  "id": "2411.10946",
  "version": "v1",
  "published": "2024-11-17T03:05:55.000Z",
  "updated": "2024-11-17T03:05:55.000Z",
  "title": "Fully nonlinear parabolic equations of real forms on Hermitian manifolds",
  "authors": [
    "Mathew George",
    "Bo Guan"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Over many decades fully nonlinear PDEs, and the complex Monge-Amp\\`ere equation in particular played a central role in the study of complex manifolds. Most previous works focused on problems that can be expressed through equations involving real $(1, 1)$ forms. As many important questions, especially those linked to higher cohomology classes in complex geometry involve real $(p, p)$ forms for $p > 1$, there is a strong need to develop PDE techniques to study them. In this paper we consider a fully nonlinear equation for $(p, p)$ forms on compact Hermitian manifolds. We establish the existence of classical solutions for a large class of these equations by a parabolic approach, proving the long-time existence and convergence of solutions to the elliptic case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-17T03:05:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K10",
      "35K55",
      "53C55",
      "58J35"
    ],
    "keywords": [
      "fully nonlinear parabolic equations",
      "real forms",
      "decades fully nonlinear pdes",
      "higher cohomology classes",
      "compact hermitian manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}