{"paper":{"title":"Finite index operators on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jose M. Espinar","submitted_at":"2009-11-19T11:45:22Z","abstract_excerpt":"We consider differential operators $L$ acting on functions on a Riemannian surface, $\\Sigma$, of the form $$L = \\Delta + V -a K ,$$where $\\Delta$ is the Laplacian of $\\Sigma$, $K$ is the Gaussian curvature, $a$ is a positive constant and $V \\in C^{\\infty}(\\Sigma)$. Such operators $L$ arise as the stability operator of $\\Sigma$ immersed in a Riemannian three-manifold with constant mean curvature (for particular choices of $V$ and $a$).\n  We assume $L$ is nonpositive acting on functions compactly supported on $\\Sigma$. If the potential, $V:= c + P $ with $c$ a nonnegative constant, verifies eith"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3767","kind":"arxiv","version":4},"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"}