{"paper":{"title":"The symplectic area of a geodesic triangle in a Hermitian symmetric space of compact type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bent {\\O}rsted, Jean-Louis Clerc, Mads Aunskj{\\ae}r Bech","submitted_at":"2018-01-21T19:19:57Z","abstract_excerpt":"Let $M$ be an irreducible Hermitian symmetric space of compact type, and let $\\omega$ be its K\\\"ahler form. For a triplet $(p_1,p_2,p_3)$ of points in $M$ we study conditions under which a geodesic triangle $\\mathcal T(p_1,p_2,p_3)$ with vertices $p_1,p_2,p_3$ can be unambiguously defined. We consider the integral $A(p_1,p_2,p_3)=\\int_\\Sigma \\omega$, where $\\Sigma$ is a surface filling the triangle $\\mathcal T(p_1,p_2,p_3)$ and discuss the dependence of $A(p_1,p_2,p_3)$ on the surface $\\Sigma$. Under mild conditions on the three points, we prove an explicit formula for $A(p_1,p_2,p_3)$ analogo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06881","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"}