{"paper":{"title":"Geometric analysis of perturbed contact instantons with Legendrian boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.SG","authors_text":"Yong-Geun Oh","submitted_at":"2022-05-24T20:24:58Z","abstract_excerpt":"In the present article, we provide analytic foundation of the following nonlinear elliptic system, called the \\emph{Hamiltonian-perturbed contact instanton equation}, $$ (du - X_H \\otimes \\gamma)^{\\pi(0,1)} = 0, \\quad\n  d(e^{g_{H, u}}u^*(\\lambda + H \\otimes \\gamma)\\circ j) = 0 $$ associated to a contact triad $(M,\\lambda,J)$ and contact Hamiltonian $H$ and its boundary value problem under the Legendrian boundary condition. (1) We identify the correct choice of the action functional for perturbed contact Hamiltonian trajectories which provides a gradient structure for the system and derive its "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.12351","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.12351/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}