{"paper":{"title":"Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.AP","authors_text":"Andreas Ros\\'en, Lashi Bandara","submitted_at":"2017-03-20T00:29:50Z","abstract_excerpt":"On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that the Atiyah-Singer Dirac operator $\\mathrm{D}_{\\mathcal B}$ in $\\mathrm{L}^{2}$ depends Riesz continuously on $\\mathrm{L}^{\\infty}$ perturbations of local boundary conditions ${\\mathcal B}$. The Lipschitz bound for the map ${\\mathcal B} \\to {\\mathrm{D}}_{\\mathcal B}(1 + {\\mathrm{D}}_{\\mathcal B}^2)^{-\\frac{1}{2}}$ depends on Lipschitz smoothness and ellipticity of ${\\mathcal B}$ and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. More generally, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06548","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"}