{"id":"https://openalex.org/W7204933594","doi":"https://doi.org/10.48550/arxiv.2608.29855","title":"Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds","display_name":"Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7204933594","doi":"https://doi.org/10.48550/arxiv.2608.29855"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29855","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29855","pdf_url":"https://arxiv.org/pdf/2608.29855","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.29855","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126703551","display_name":"Xiaolong Hans Han","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Han, Xiaolong Hans","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5148940485","display_name":"Bohan Yang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Bohan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.6675000190734863,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.6675000190734863,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.2087000012397766,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.05130000039935112,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/closed-geodesics","display_name":"closed geodesics","score":0.9440000057220459},{"id":"https://openalex.org/keywords/simple-closed-geodesics","display_name":"simple closed geodesics","score":0.8140000104904175},{"id":"https://openalex.org/keywords/growth-rate","display_name":"growth rate","score":0.7210000157356262},{"id":"https://openalex.org/keywords/finite-volume-hyperbolic-manifolds","display_name":"finite volume hyperbolic manifolds","score":0.9620000123977661},{"id":"https://openalex.org/keywords/unit-tangent-bundle","display_name":"unit tangent bundle","score":0.9380000233650208},{"id":"https://openalex.org/keywords/density","display_name":"density","score":0.5559999942779541}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.7896000146865845},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7563999891281128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6448000073432922},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4546000063419342},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C55862258","wikidata":"https://www.wikidata.org/wiki/Q1017238","display_name":"Hyperbolic coordinates","level":5,"score":0.3562000095844269},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.33250001072883606},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.3077999949455261},{"id":"https://openalex.org/C129671197","wikidata":"https://www.wikidata.org/wiki/Q5957770","display_name":"Hyperbolic 3-manifold","level":5,"score":0.3001999855041504},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28999999165534973},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.27379998564720154},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2599000036716461}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29855","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29855","pdf_url":"https://arxiv.org/pdf/2608.29855","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.29855","doi":"https://doi.org/10.48550/arxiv.2608.29855","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29855","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.29855","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29855","pdf_url":"https://arxiv.org/pdf/2608.29855","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204933594.pdf","grobid_xml":"https://content.openalex.org/works/W7204933594.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2530798852","https://openalex.org/W3208489764","https://openalex.org/W4407131471","https://openalex.org/W4410567639","https://openalex.org/W7141248772","https://openalex.org/W7204918634"],"related_works":["https://openalex.org/W1982041505","https://openalex.org/W1590139234","https://openalex.org/W3208489764","https://openalex.org/W7204918634","https://openalex.org/W2079027649","https://openalex.org/W7216090531","https://openalex.org/W1632546858","https://openalex.org/W1969295985","https://openalex.org/W2944489803","https://openalex.org/W2124004615"],"abstract_inverted_index":{"Let":[0],"$M$":[1,35],"be":[2],"a":[3],"finite-volume":[4],"hyperbolic":[5,46],"$d$-manifold":[6],"with":[7],"$d\\ge3$.":[8],"We":[9],"prove":[10],"that":[11,42],"the":[12,50,61],"number":[13],"of":[14,48],"primitive":[15,31],"nonsimple":[16,55],"closed":[17,32,56],"geodesics":[18,57],"has":[19],"exponential":[20],"growth":[21],"rate":[22],"strictly":[23],"smaller":[24],"than":[25],"$d-1$.":[26],"Consequently,":[27],"asymptotically":[28],"almost":[29],"every":[30],"geodesic":[33],"in":[34,60],"is":[36],"simple.":[37],"In":[38],"contrast,":[39],"we":[40],"show":[41],"on":[43],"an":[44],"arithmetic":[45],"manifold":[47],"type~I,":[49],"unit":[51,62],"vectors":[52],"tangent":[53,63],"to":[54],"are":[58],"dense":[59],"bundle.":[64]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
