{"paper":{"title":"Concavity of the Lagrangian Phase Operator and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Sebastien Picard, Tristan C. Collins, Xuan Wu","submitted_at":"2016-07-25T10:19:05Z","abstract_excerpt":"We study the Dirichlet problem for the Lagrangian phase operator, in both the real and complex setting. Our main result states that if $\\Omega$ is a compact domain in $\\mathbb{R}^{n}$ or $\\mathbb{C}^n$, then there exists a solution to the Dirichlet problem with right-hand side $h(x)$ satisfying $|h(x)| > (n-2)\\frac{\\pi}{2}$ and boundary data $\\phi$ if and only if there exists a subsolution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07194","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"}