{"paper":{"title":"Analysis of Contact Cauchy-Riemann maps I: a priori $C^k$ estimates and asymptotic convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Rui Wang, Yong-Geun Oh","submitted_at":"2012-12-20T18:41:39Z","abstract_excerpt":"In the present article, we develop the analysis of the following nonlinear elliptic system of equations $$ \\bar\\partial^\\pi w = 0, \\, d(w^*\\lambda \\circ j) = 0 $$ first introduced by Hofer, associated to each given contact triad $(M,\\lambda,J)$ on a contact manifold $(M,\\xi)$. We directly work with this elliptic system on the contact manifold without involving the symplectization process. We establish the local a priori $C^k$ coercive pointwise estimates for all $k \\geq 2$ in terms of $\\|dw\\|_{C^0}$ by doing tensorial calculations on contact manifold itself using the contact triad connection i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5186","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"}