{"paper":{"title":"Measure Upper Bounds of Nodal Sets of Robin Eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fang Liu, Long Tian, Xiaoping Yang","submitted_at":"2018-01-07T02:32:20Z","abstract_excerpt":"In this paper, we obtain the upper bounds for the Hausdorff measures of nodal sets of eigenfunctions with the Robin boundary conditions, i.e.,\n  \\begin{equation*} {\\left\\{\\begin{array}{l}\n  \\triangle u+\\lambda u=0,\\quad in\\quad \\Omega,\\\\ u_{\\nu}+\\mu u=0,\\quad on\\quad\\partial\\Omega, \\end{array} \\right.} \\end{equation*} where the domain $\\Omega\\subseteq\\mathbb{R}^n$, $u_{\\nu}$ means the derivative of $u$ along the outer normal direction of $\\partial\\Omega$. We show that, if $\\Omega$ is bounded and analytic, and the corresponding eigenvalue $\\lambda$ is large enough,then the measure upper bounds "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02114","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":""},"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"}