{"paper":{"title":"Neumann Data Mass on Perturbed Triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Hans Christianson, Jin Xi","submitted_at":"2019-08-07T22:45:40Z","abstract_excerpt":"Based on a previous paper [Chr17] on Neumann data for Dirichlet eigenfunctions on triangles, we extend the study in two ways. First, we investigate the (semi-classical) Neumann data mass on perturbed triangles. Specifically, we replace one side of a triangle by adding a smooth perturbation, and assume that the disparity between the perturbation and the original side is bounded by a small value $\\epsilon$. Second, we add a small $\\epsilon$ sized potential to the (semi-classical) Laplacian and see how the results change on triangles. In both cases, we find that the $L^2$ norm of Neumann data on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02863","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/1908.02863/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"}