{"paper":{"title":"Conformal covariance of the Liouville quantum gravity metric for $\\gamma \\in (0,2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP"],"primary_cat":"math.PR","authors_text":"Ewain Gwynne, Jason Miller","submitted_at":"2019-05-01T17:02:23Z","abstract_excerpt":"For $\\gamma \\in (0,2)$, $U\\subset \\mathbb C$, and an instance $h$ of the Gaussian free field (GFF) on $U$, the $\\gamma$-Liouville quantum gravity (LQG) surface associated with $(U,h)$ is formally described by the Riemannian metric tensor $e^{\\gamma h} (dx^2 + dy^2)$ on $U$. Previous work by the authors showed that one can define a canonical metric (distance function) $D_h$ on $U$ associated with a $\\gamma$-LQG surface. We show that this metric is conformally covariant in the sense that it respects the coordinate change formula for $\\gamma$-LQG surfaces. That is, if $U,\\widetilde{U}$ are domain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00384","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.00384/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"}