{"paper":{"title":"Critical points of second Neumann eigenfunctions on some convex domains in two-dimensional space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haiyun Deng, Xiaoping Yang, Xuyong Jiang","submitted_at":"2026-07-20T12:32:46Z","abstract_excerpt":"In this paper, we investigate critical points of second Neumann eigenfunctions on convex domains in the two-dimensional space forms. We approach this problem from three complementary perspectives: spectral and geometric conditions; explicit quantitative location restrictions; the hot spots constant. Precisely, for the spectral and geometric conditions, we prove that if a convex domain $\\Omega$ is contained in the hemisphere and satisfies $\\mu_{2}(\\Omega)\\leq 2$, then its second Neumann eigenfunction has no interior critical points. Beyond this, we establish a unified diameter-based criterion $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17882","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/2607.17882/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"}