{"paper":{"title":"Integral estimates for the trace of symmetric operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Heudson Mirandola, Marcio Batista","submitted_at":"2012-03-31T15:49:55Z","abstract_excerpt":"Let $\\Phi:TM\\to TM$ be a positive-semidefinite symmetric operator of class $C^1$ defined on a complete non-compact manifold $M$ isometrically immersed in a Hadamard space $\\bar{M}$. In this paper, we given conditions on the operator $\\Phi$ and on the second fundamental form to guarantee that either $\\Phi\\equiv 0$ or the integral $\\int_M \\mathrm{tr}\\,\\Phi dM$ is infinite. We will given some applications. The first one says that if $M$ admits an integrable distribution whose integrals are minimal submanifolds in $\\bar{M}$ then the volume of $M$ must be infinite. Another application states that i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0108","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"}