{"paper":{"title":"The deformation of symplectic critical surfaces in a K\\\"ahler surface-I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jiayu Li, Jun Sun, Xiaoli Han","submitted_at":"2015-04-16T08:35:44Z","abstract_excerpt":"In this paper we derive the Euler-Lagrange equation of the functional $L_\\beta=\\int_\\Sigma\\frac{1}{\\cos^\\beta\\alpha}d\\mu, ~~\\beta\\neq -1$ in the class of symplectic surfaces. It is $\\cos^3\\alpha {\\bf{H}}=\\beta(J(J\\nabla\\cos\\alpha)^\\top)^\\bot$, which is an elliptic equation when $\\beta\\geq 0$. We call such a surface a $\\beta$-symplectic critical surface. We first study the properties for each fixed $\\beta$-symplectic critical surface and then prove that the set of $\\beta$ where there is a stable $\\beta$-symplectic critical surface is open. We believe it should be also closed. As a precise examp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04138","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"}