{"paper":{"title":"Upper semi-continuity of the Royden-Kobayashi pseudo-norm, a counterexample for H\\\"olderian almost complex structures","license":"","headline":"","cross_cats":["math.SG"],"primary_cat":"math.CV","authors_text":"Jean-Pierre Rosay, Sergey Ivashkovich, Sergey Pinchuk","submitted_at":"2004-02-20T08:12:41Z","abstract_excerpt":"If $X$ is an almost complex manifold, with an almost complex structure $J$ of class $\\CC^\\alpha$, for some $\\alpha >0$, for every point $p\\in X$ and every tangent vector $V$ at $p$, there exists a germ of $J$-holomorphic disc through $p$ with this prescribed tangent vector. This existence result goes back to Nijenhuis-Woolf. All the $J$ holomorphic curves are of class $\\CC^{1,\\alpha}$ in this case.\n  Then, exactly as for complex manifolds one can define the Royden-Kobayashi pseudo-norm of tangent vectors. The question arises whether this pseudo-norm is an upper semi-continuous function on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402331","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"}