{"paper":{"title":"Conformal Barycenters in Quaternionic Hyperbolic Balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Wensheng Cao, Zhijian Ge","submitted_at":"2026-05-20T03:28:08Z","abstract_excerpt":"We extend the notion of conformal barycenter, recently introduced by\n  Ja\\v{c}imovi\\'{c} and Kalaj for the complex hyperbolic ball, to the\n  quaternionic unit ball $\\BH$. The quaternionic\n  conformal barycenter of a measurable set $D$ with finite hyperbolic\n  measure and finite first moment is defined as the unique point $c$ such that\n  $\\int_D \\Phi_c(q)\\, \\dLam(q) = \\mathbf{0}$, where\n  $\\Phi_c$ is the quaternionic Hua involution exchanging $0$ and $c$.\n  Equivalently, it is the unique minimum of the energy functional\n  $G(x) = \\int_D \\log\\cosh^2\\!\\big(\\frac12 d_H(x,y)\\big)\\, \\dLam(y)$.\n  We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20662","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20662/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"}