{"paper":{"title":"Discreteness of spectrum for the $\\overline\\partial$-Neumann Laplacian on manifolds of bounded geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Franz Berger","submitted_at":"2018-08-08T11:42:54Z","abstract_excerpt":"For a Hermitian holomorphic vector bundle over a Hermitian manifold, we consider the Dolbeault Laplacian with $\\overline\\partial$-Neumann boundary conditions, which is a self-adjoint operator on the space of square-integrable differential forms with values in the given holomorphic bundle. We argue that some known results on the spectral properties of this operator on pseudoconvex domains in $\\mathbb C^n$ continue to hold on K\\\"ahler manifolds satisfying certain bounded geometry assumptions. In particular, we will consider the Dolbeault complex for forms with values in a line bundle, where know"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02730","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":""},"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"}