{"paper":{"title":"Interior nodal sets of Steklov eigenfunctions on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Jiuyi Zhu","submitted_at":"2015-07-02T15:20:48Z","abstract_excerpt":"We investigate the interior nodal sets $\\mathcal{N}_\\lambda$ of Steklov eigenfunctions on connected and compact surfaces with boundary. The optimal vanishing order of Steklov eigenfunctions is shown be $C\\lambda$. The singular sets $\\mathcal{S}_\\lambda$ are finite points on the nodal sets. We are able to prove that the Hausdorff measure $H^0(\\mathcal{S}_\\lambda)\\leq C\\lambda^2$. Furthermore, we obtain an upper bound for the measure of interior nodal sets $H^1(\\mathcal{N}_\\lambda)\\leq C\\lambda^{\\frac{3}{2}}$. Here those positive constants $C$ depend only on the surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00621","kind":"arxiv","version":2},"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"}