{"paper":{"title":"Homotopy type of manifolds with partially horoconvex boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Changwei Xiong","submitted_at":"2018-09-19T01:57:07Z","abstract_excerpt":"Let $M$ be an $n$-dimensional compact connected manifold with boundary, $\\kappa>0$ a constant and $1\\leq q\\leq n-1$ an integer. We prove that $M$ supports a Riemannian metric with the interior $q$-curvature $K_q\\geq -q\\kappa^2$ and the boundary $q$-curvature $\\Lambda_q\\geq q\\kappa$, if and only if $M$ has the homotopy type of a CW complex with a finite number of cells with dimension $\\leq (q-1)$. Moreover, any Riemannian manifold $M$ with sectional curvature $K\\geq -\\kappa^2$ and boundary principal curvature $\\Lambda\\geq \\kappa$ is diffeomorphic to the standard closed $n$-ball."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06982","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"}