{"paper":{"title":"Boundary value problems for noncompact boundaries of Spin$^c$ manifolds and spectral estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DG","authors_text":"Nadine Gro{\\ss}e, Roger Nakad","submitted_at":"2012-07-19T06:58:24Z","abstract_excerpt":"We study boundary value problems for the Dirac operator on Riemannian Spin$^c$ manifolds of bounded geometry and with noncompact boundary. This generalizes a part of the theory of boundary value problems by C. B\\\"ar and W. Ballmann for complete manifolds with closed boundary. As an application, we derive the lower bound of Hijazi-Montiel-Zhang, involving the mean curvature of the boundary, for the spectrum of the Dirac operator on the noncompact boundary of a Spin$^c$ manifold. The limiting case is then studied and examples are then given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4568","kind":"arxiv","version":3},"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"}