{"paper":{"title":"(1,1) forms with specified Lagrangian phase: A priori estimates and algebraic obstructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Adam Jacob, Shing-Tung Yau, Tristan C. Collins","submitted_at":"2015-08-08T18:01:02Z","abstract_excerpt":"Let $(X,\\alpha)$ be a K\\\"ahler manifold of dimension n, and let $[\\omega] \\in H^{1,1}(X,\\mathbb{R})$. We study the problem of specifying the Lagrangian phase of $\\omega$ with respect to $\\alpha$, which is described by the nonlinear elliptic equation \\[ \\sum_{i=1}^{n} \\arctan(\\lambda_i)= h(x) \\] where $\\lambda_i$ are the eigenvalues of $\\omega$ with respect to $\\alpha$. When $h(x)$ is a topological constant, this equation corresponds to the deformed Hermitian-Yang-Mills (dHYM) equation, and is related by Mirror Symmetry to the existence of special Lagrangian submanifolds of the mirror. We intro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01934","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"}