{"paper":{"title":"Exact Poincare Constants in n-dimensional Annuli","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bernd Rummler, Gudrun Th\\\"ater, Michael Ruzicka","submitted_at":"2026-06-03T11:50:09Z","abstract_excerpt":"We study $n$-dimensional annuli for $n\\,\\in\\,\\{2,\\dots,N\\}$ with $N\\,<\\,\\infty$.\n  We choose a non-dimensional setting such that for any fixed $n\n  $ and given number ${\\cal A}>0$ the\n  annuli ${\\Omega}_{(n),\\cal A}$ are defined as space between two concentrical balls with radii ${\\cal A}/2$ and ${\\cal A}/2 +1$ in ${\n  R}^{n}$. For these geometries we provide calculated (precise) Poincar\\'e constants. These depend on ${\\cal A}$ and the dimension $n$. Additionally we find a direct match of the Poincar\\'e constants for solenoidal vector fields in ${R}^{n}$ and the Poincar\\'e constants for scalar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04765","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/2606.04765/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"}