{"id":"https://openalex.org/W7204238985","doi":"https://doi.org/10.1142/s1793525326500573","title":"A Sharp Hyperbolic Volume Bound for Hypersurfaces in M3 \u00d7 \ud835\udd4a1","display_name":"A Sharp Hyperbolic Volume Bound for Hypersurfaces in M3 \u00d7 \ud835\udd4a1","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7204238985","doi":"https://doi.org/10.1142/s1793525326500573"},"language":"en","primary_location":{"id":"doi:10.1142/s1793525326500573","doi":"https://doi.org/10.1142/s1793525326500573","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793525326500573","pdf_url":null,"source":{"id":"https://openalex.org/S167996400","display_name":"Journal of Topology and Analysis","issn_l":"1793-5253","issn":["1793-5253","1793-7167"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Topology and Analysis","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.24057","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021298004","display_name":"Lizhi Chen","orcid":"https://orcid.org/0009-0005-0323-7913","observed_orcids":["https://orcid.org/0009-0005-0323-7913","https://orcid.org/0000-0002-0635-5860"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lizhi Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5144329489","display_name":"Kuntao Jin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kuntao Jin","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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.5903000235557556,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.5903000235557556,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.34299999475479126,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.05389999970793724,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperbolic-3-manifolds","display_name":"hyperbolic 3-manifolds","score":0.9240000247955322},{"id":"https://openalex.org/keywords/hypersurfaces","display_name":"hypersurfaces","score":0.8679999709129333},{"id":"https://openalex.org/keywords/embedded-hypersurfaces","display_name":"embedded hypersurfaces","score":0.7960000038146973},{"id":"https://openalex.org/keywords/product-metrics","display_name":"product metrics","score":0.6890000104904175},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"scalar curvature","score":0.777999997138977}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8277000188827515},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.8111000061035156},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.7390999794006348},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.657800018787384},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5950999855995178},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5519999861717224},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48410001397132874},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.4643000066280365},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44369998574256897},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4406999945640564},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.3917999863624573},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.3779999911785126},{"id":"https://openalex.org/C117855890","wikidata":"https://www.wikidata.org/wiki/Q3042004","display_name":"Hyperbolic set","level":2,"score":0.3675000071525574},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30869999527931213},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2969000041484833},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.2872999906539917},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.2827000021934509},{"id":"https://openalex.org/C154497576","wikidata":"https://www.wikidata.org/wiki/Q7247777","display_name":"Product metric","level":3,"score":0.2816999852657318},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.28029999136924744}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s1793525326500573","doi":"https://doi.org/10.1142/s1793525326500573","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793525326500573","pdf_url":null,"source":{"id":"https://openalex.org/S167996400","display_name":"Journal of Topology and Analysis","issn_l":"1793-5253","issn":["1793-5253","1793-7167"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Topology and Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2608.24057","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24057","pdf_url":"https://arxiv.org/pdf/2608.24057","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.2608.24057","doi":"https://doi.org/10.48550/arxiv.2608.24057","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.24057","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:2608.24057","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24057","pdf_url":"https://arxiv.org/pdf/2608.24057","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204238985.pdf","grobid_xml":"https://content.openalex.org/works/W7204238985.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2949125866","https://openalex.org/W4392737161","https://openalex.org/W3214203450","https://openalex.org/W7096775122","https://openalex.org/W567029745","https://openalex.org/W1528055422","https://openalex.org/W2007519272","https://openalex.org/W4414593813","https://openalex.org/W2964259375","https://openalex.org/W1989101321"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,13,28,35,45,54,60,68,75,79,90,94,100,109,121,125],"see":[2,14,29,36,46,55,61,69,76,80,91,95,101,110,122,126],"text]":[3,30,47,56,70,77,96,123],"be":[4],"a":[5,18,49,115],"closed":[6,65],"oriented":[7],"hyperbolic":[8],"three-manifold":[9],"normalized":[10],"so":[11],"that":[12],"text].":[15,81,102,127],"We":[16],"prove":[17],"sharp":[19],"lower":[20],"bound":[21,83],"for":[22,107],"the":[23,32,41,72,87,118],"volume":[24],"of":[25],"hypersurfaces":[26],"in":[27],"representing":[31,71],"slice":[33,73,119],"class":[34,74],"text],":[37,62,92,111],"and":[38,124],"we":[39],"classify":[40],"equality":[42,105],"case.":[43],"If":[44],"is":[48,84],"smooth":[50],"Riemannian":[51],"metric":[52,89,98],"on":[53,99],"with":[57,93],"scalar":[58],"curvature":[59],"then":[63,112],"every":[64],"embedded":[66],"hypersurface":[67],"satisfies":[78],"The":[82],"attained":[85],"by":[86],"product":[88],"any":[97],"Conversely,":[103],"if":[104],"holds":[106],"some":[108],"up":[113],"to":[114],"diffeomorphism":[116],"preserving":[117],"class,":[120]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-27T00:00:00"}