{"paper":{"title":"Weyl asymptotics for singular metrics with a variable boundary degeneracy exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"CaGE), Charlotte Dietze (LJLL (UMR\\_7598), CNRS), Emmanuel Tr\\'elat (LJLL (UMR\\_7598), Yves Colin De Verdi\\`ere (IF)","submitted_at":"2026-03-16T13:24:34Z","abstract_excerpt":"We consider a compact smooth manifold $X$ of dimension $n+1$ with boundary $M=\\partial X$. In a collar neighborhood of $M$, we assume that the metric has the form $g=u^{-\\alpha}\\bar g$, where $u$ is a boundary defining function, $\\alpha\\in C^1(M;[0,2))$ and $\\bar g$ is a $C^1$ Riemannian metric up to $M$. Since $\\alpha<2$, the boundary lies at finite $g$-distance and $(X,g)$ is a singular metric space. We study the Weyl asymptotics of the Friedrichs Laplacian $\\triangle\\_g$ when the degeneracy exponent $\\alpha$ varies along $M$. If the maximum $\\alpha\\_{\\mathrm{max}}$ of $\\alpha$ on $M$ is str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.15256","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.15256/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"}