{"paper":{"title":"Gaussian Harmonic Forms and Two-Dimensional Self-Shrinkers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Matthew McGonagle","submitted_at":"2012-03-30T03:12:04Z","abstract_excerpt":"We consider 2-dimensional orientable self-shrinkers $\\Sigma$ for the Mean Curvature Flow of polynomial volume growth immersed in $\\mathbb R^n$. We look at closed one forms minimizing the norm $\\int_\\Sigma \\eterm |\\omega|^2$ in their cohomology class. Any closed form satisfying the Euler-Lagrange equation for this minimization will be called a Gaussian Harmonic one Form (GHF).\n  We then use these forms to show that if such a $\\Sigma$ has genus $\\geq 1,$ then we have a lower bound on the supremum norm of $A^2$. GHF's may also be applied to create an upperbound for the lowest eigenvalue of the op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6704","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"}