{"paper":{"title":"Local asymptotics near a smooth boundary point and estimates for a hyperbolic-type metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.MG","authors_text":"Pritam Naskar","submitted_at":"2026-07-29T06:42:44Z","abstract_excerpt":"In this paper, we investigate the local boundary behaviour of a recently developed hyperbolic-type metric $m_D$. First, employing a boundary-flattening technique and local behaviour of $m_D$-geodesics, we establish its asymptotic formula near any $C^1$-smooth boundary point. Next, we introduce a metric quantity analogous to the Nikolov--Andreev metric and show that $m_D$ is the inner metric associated with it. Finally, by establishing a sharp two-sided comparison inequality, we obtain an improved lower bound for the $m_D$-metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26524","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/2607.26524/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"}