{"paper":{"title":"Lagrangian potential theory and a Lagrangian equation of Monge-Amp\\`ere type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"F. Reese Harvey, H. Blaine Lawson Jr","submitted_at":"2017-12-10T13:36:56Z","abstract_excerpt":"The purpose of this paper is to establish a Lagrangian potential theory, analogous to the classical pluripotential theory, and to define and study a Lagrangian differential operator of Monge-Ampere type. This development is new even in ${\\bf C}^n$. However, it applies quite generally -- perhaps most importantly to symplectic manifolds equipped with a Gromov metric.\n  The Lagrange Monge-Ampere operator is an explicit polynomial on ${\\rm Sym}^2(TX)$ whose principle branch defines the space of Lag-harmonics. Interestingly the operator depends only on the Laplacian and the SKEW-Hermitian part of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03525","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":""},"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"}