{"paper":{"title":"Wellposedness of nonlinear flows on manifolds of bounded geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.AP","authors_text":"Christine Guenther, Eric Bahuaud, James Isenberg, Rafe Mazzeo","submitted_at":"2022-10-28T04:28:50Z","abstract_excerpt":"We present simple conditions which ensure that a strongly elliptic operator $L$ generates an analytic semigroup on H\\\"older spaces on an arbitrary complete manifold of bounded geometry. This is done by establishing the equivalent property that $L$ is \"sectorial\", a condition that specifies the decay of the resolvent $(\\lambda I - L)^{-1}$ as $\\lambda$ diverges from the H\\\"older spectrum of $L$. As one step, we prove existence of this resolvent if $\\lambda$ is sufficiently large, and on this general class of manifolds, use a geometric microlocal version of the semiclassical pseudodifferential c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.15886","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/2210.15886/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"}