{"paper":{"title":"The first conformal Dirac eigenvalue on 2-dimensional tori","license":"","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DG","authors_text":"Bernd Ammann, Emmanuel Humbert","submitted_at":"2004-12-20T18:15:16Z","abstract_excerpt":"Let M be a compact manifold with a spin structure \\chi and a Riemannian metric g. Let \\lambda_g^2 be the smallest eigenvalue of the square of the Dirac operator with respect to g and \\chi. The \\tau-invariant is defined as \\tau(M,\\chi):= sup inf \\sqrt{\\lambda_g^2} Vol(M,g)^{1/n} where the supremum runs over the set of all conformal classes on M, and where the infimum runs over all metrics in the given class. We show that \\tau(T^2,\\chi)=2\\sqrt{\\pi} if \\chi is ``the'' non-trivial spin structure on T^2. In order to calculate this invariant, we study the infimum as a function on the spin-conformal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412409","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":""},"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"}