{"paper":{"title":"Strict concavity of the growth indicator function for relatively Anosov groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR","math.GT"],"primary_cat":"math.DG","authors_text":"Andrew Zimmer, Dongryul M. Kim, Hee Oh","submitted_at":"2026-07-15T12:21:23Z","abstract_excerpt":"Let $\\Gamma$ be a discrete subgroup of a connected semisimple real algebraic group of higher rank. The growth indicator function $\\psi_\\Gamma$ records the directional exponential growth of the Cartan projections of elements of $\\Gamma$ in the positive Weyl chamber $\\mathfrak a^+$. We prove that if $\\Gamma$ is a non-elementary relatively Borel Anosov group, then $\\psi_\\Gamma$ is strictly concave on non-collinear directions. We prove this by establishing the $\\mathcal C^1$-smoothness of the Manhattan hypersurface, defined as the unit level set of the critical-exponent map $\\phi\\mapsto\\delta^\\phi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13760","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/2607.13760/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"}