{"paper":{"title":"Explicit fundamental gap estimates for some convex domains in $\\mathbb H^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alina Stancu, Guofang Wei, Julie Clutterbuck, Theodora Bourni, Valentina-Mira Wheeler, Xuan Hien Nguyen","submitted_at":"2019-11-28T22:57:30Z","abstract_excerpt":"Motivated by an example of Shih, we compute the fundamental gap of a family of convex domains in the hyperbolic plane $\\mathbb H^2$, showing that for some of them $\\lambda_2 - \\lambda_1 < \\frac{3\\pi^2}{D^2}$, where $D$ is the diameter of the domain and $\\lambda_1$, $\\lambda_2$ are the first and second Dirichlet eigenvalues of the Laplace operator on the domain. The result contrasts with what is known in $\\mathbb R^n $ or $\\mathbb S^n$, where $\\lambda_2 - \\lambda_1 \\geq \\frac{3 \\pi^2}{D^2}$ for convex domains. We also show that the fundamental gap of the example in Shih's article is still great"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.12892","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/1911.12892/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"}