{"paper":{"title":"Laplacian flow for closed G_2 structures: Shi-type estimates, uniqueness and compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jason D. Lotay, Yong Wei","submitted_at":"2015-04-28T07:37:27Z","abstract_excerpt":"We develop foundational theory for the Laplacian flow for closed G_2 structures which will be essential for future study. (1). We prove Shi-type derivative estimates for the Riemann curvature tensor Rm and torsion tensor T along the flow, i.e. that a bound on $\\Lambda(x,t)=\\left(|\\nabla T(x,t)|_{g(t)}^2+|Rm(x,t)|_{g(t)}^2\\right)^{\\frac 12}$ will imply bounds on all covariant derivatives of Rm and T. (2). We show that $\\Lambda(x,t)$ will blow up at a finite-time singularity, so the flow will exist as long as $\\Lambda(x,t)$ remains bounded. (3). We give a new proof of forward uniqueness and prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07367","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"}