{
  "id": "1912.12071",
  "version": "v1",
  "published": "2019-12-27T12:34:36.000Z",
  "updated": "2019-12-27T12:34:36.000Z",
  "title": "Estimates of bubbling solutions of $SU(3)$ Toda systems at critical parameters-Part 1",
  "authors": [
    "Lina Wu",
    "Lei Zhang"
  ],
  "comment": "40 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "For regular $SU(3)$ Toda systems defined on Riemann surface, we initiate the study of bubbling solutions if parameters $(\\rho_1^k,\\rho_2^k)$ are both tending to critical positions: $(\\rho_1^k,\\rho_2^k)\\to (4\\pi, 4\\pi N)$ or $(4\\pi N, 4\\pi)$ ($N>0$ is an integer). We prove that there are at most three formations of bubbling profiles, and for each formation we identify leading terms of $\\rho_1^k-4\\pi$ and $\\rho_2^k-4\\pi N$, locations of blowup points and comparison of bubbling heights with sharp precision. The results of this article will be used as substantial tools for a number of degree counting theorems, critical point at infinity theory in the future.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-27T12:34:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J47",
      "58J05"
    ],
    "keywords": [
      "toda systems",
      "bubbling solutions",
      "critical parameters-part",
      "infinity theory",
      "blowup points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}