{"paper":{"title":"Nondegeneracy of positive solutions for critical Hartree equation on Heisenberg group and it's applications","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Minbo Yang, Shuijin Zhang","submitted_at":"2025-08-11T07:46:35Z","abstract_excerpt":"We study the uniqueness and nondegeneracy of positive bubble solutions for the generalized energy-critical Hartree equation on the Heisenberg group $\\mathbb{H}^{n}$, \\begin{equation}\\label{0.1}\n  -\\Delta_{\\mathbb{H}}u=\\left(\\int_{\\mathbb{H}^{n}}\\frac{|u(\\eta)|^{Q^{\\ast}_{\\mu}}}{|\\eta^{-1}\\xi|^{\\mu}}\\mathrm{d}\\eta\\right)|u|^{Q^{\\ast}_{\\mu}-2}u,~~~\\xi,\\eta\\in\\mathbb{H}^{n}, \\end{equation} where $\\Delta_{\\mathbb{H}}$ represents the Kohn Laplacian, $u(\\eta)$ is a real-valued function, $Q=2n+2$ is the homogeneous dimension of $\\mathbb{H}^{n}$, $\\mu\\in (0,Q)$ is a real parameter and $Q^{\\ast}_{\\mu}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07719","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.07719/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}