{"paper":{"title":"Heinz mean curvature estimates in warped product spaces $M\\times_{e^{\\psi}}N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Isabel M.C. Salavessa","submitted_at":"2017-01-01T21:40:18Z","abstract_excerpt":"If a graph submanifold $(x,f(x))$ of a Riemannian warped product space $(M^m\\times_{e^{\\psi}}N^n,\\tilde{g}=g+e^{2\\psi}h)$ is immersed with parallel mean curvature $H$, then we obtain a Heinz type estimation of the mean curvature. Namely, on each compact domain $D$ of $M$, $m\\|H\\|\\leq \\frac{A_{\\psi}(\\partial D)}{V_{\\psi}(D)}$ holds, where $A_{\\psi}(\\partial D)$ and $V_{\\psi}(D)$ are the ${\\psi}$-weighted area and volume, respectively. In particular, $H=0$ if $(M,g)$ has zero weighted Cheeger constant, a concept recently introduced by D.\\ Impera et al.\\ (\\cite{[Im]}). This generalizes the known "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00290","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"}