{"paper":{"title":"A holographic principle for the existence of parallel spinor fields and an inequality of Shi-Tam type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Oussama Hijazi, Sebasti\\'an Montiel","submitted_at":"2015-02-17T10:55:48Z","abstract_excerpt":"Suppose that $\\Sigma=\\partial M$ is the $n$-dimensional boundary of a connected compact Riemannian spin manifold $( M,\\langle\\;,\\;\\rangle)$ with non-negative scalar curvature, and that the (inward) mean curvature $H$ of $\\Sigma$ is positive. We show that the first eigenvalue of the Dirac operator of the boundary corresponding to the conformal metric $\\langle\\;,\\;\\rangle_H=H^2\\langle\\;,\\;\\rangle$ is at least $n/2$ and equality holds if and only if there exists a parallel spinor field on $ M$. As a consequence, if $\\Sigma$ admits an isometric and isospin immersion $\\phi$ with mean curvature $H_0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04859","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"}