{"paper":{"title":"Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Esko Heinonen, Ilkka Holopainen, Jean-Baptiste Casteras","submitted_at":"2015-04-21T10:34:52Z","abstract_excerpt":"We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan-Hadamard manifold $M$ whose radial sectional curvatures outside a compact set satisfy an upper bound $$K(P)\\le - \\frac{\\phi(\\phi-1)}{r(x)^2}$$ and a pointwise pinching condition $$|K(P)|\\le C_K|K(P')|$$ for some constants $\\phi>1$ and $C_K\\ge 1$, where $P$ and $P'$ are any 2-dimensional subspaces of $T_xM$ containing the (radial) vector $\\nabla r(x)$ and $r(x)=d(o,x)$ is the distance to a fixed point $o\\in M$. We solve the asymptotic Dirichlet problem with any continuous boundary data for dimensions $n>4/\\phi+"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05378","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"}