{"id":"https://openalex.org/W3142829698","doi":"https://doi.org/10.48550/arxiv.2104.03181","title":"Moebius structures, hyperbolic ends and $k$-surfaces in hyperbolic space","display_name":"Moebius structures, hyperbolic ends and $k$-surfaces in hyperbolic space","publication_year":2021,"publication_date":"2021-04-07","ids":{"openalex":"https://openalex.org/W3142829698","doi":"https://doi.org/10.48550/arxiv.2104.03181","mag":"3142829698"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2104.03181","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.03181","pdf_url":"https://arxiv.org/pdf/2104.03181","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2104.03181","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067833918","display_name":"Graham Smith","orcid":"https://orcid.org/0000-0001-5369-8279","observed_orcids":["https://orcid.org/0000-0001-5369-8279"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Smith, Graham","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5067833918"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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":0.9448000192642212,"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":0.9448000192642212,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.02710000053048134,"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/T12504","display_name":"Mathematics and Applications","score":0.00559999980032444,"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/mobius-structures","display_name":"M\u00f6bius structures","score":0.996999979019165},{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"hyperbolic geometry","score":0.8029999732971191}],"concepts":[{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.7058996558189392},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.6051779985427856},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.5759767889976501},{"id":"https://openalex.org/C82673646","wikidata":"https://www.wikidata.org/wiki/Q2246553","display_name":"Hyperbolic triangle","level":4,"score":0.5585802793502808},{"id":"https://openalex.org/C55862258","wikidata":"https://www.wikidata.org/wiki/Q1017238","display_name":"Hyperbolic coordinates","level":5,"score":0.5277659893035889},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.5274325013160706},{"id":"https://openalex.org/C39308205","wikidata":"https://www.wikidata.org/wiki/Q7880612","display_name":"Ultraparallel theorem","level":5,"score":0.474725604057312},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45616039633750916},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.4516557455062866},{"id":"https://openalex.org/C97654310","wikidata":"https://www.wikidata.org/wiki/Q574023","display_name":"Hyperbolic tree","level":4,"score":0.4365497827529907},{"id":"https://openalex.org/C139966315","wikidata":"https://www.wikidata.org/wiki/Q1003216","display_name":"Hyperbolic angle","level":5,"score":0.4360314607620239},{"id":"https://openalex.org/C129671197","wikidata":"https://www.wikidata.org/wiki/Q5957770","display_name":"Hyperbolic 3-manifold","level":5,"score":0.4239423871040344},{"id":"https://openalex.org/C40020168","wikidata":"https://www.wikidata.org/wiki/Q7310818","display_name":"Relatively hyperbolic group","level":4,"score":0.4145851731300354},{"id":"https://openalex.org/C51691630","wikidata":"https://www.wikidata.org/wiki/Q3925833","display_name":"Hyperbolic equilibrium point","level":4,"score":0.3921911120414734},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3896363377571106},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35569316148757935},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32455602288246155},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3242500424385071},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14486294984817505},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.07826489210128784},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2104.03181","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.03181","pdf_url":"https://arxiv.org/pdf/2104.03181","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.2104.03181","doi":"https://doi.org/10.48550/arxiv.2104.03181","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2104.03181","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2104.03181","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.03181","pdf_url":"https://arxiv.org/pdf/2104.03181","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W41778808","https://openalex.org/W1495768073","https://openalex.org/W1520325860","https://openalex.org/W1533061882","https://openalex.org/W1935901699","https://openalex.org/W1985776754","https://openalex.org/W2009039081","https://openalex.org/W2044720368","https://openalex.org/W2047223617","https://openalex.org/W2068511661","https://openalex.org/W2076035020","https://openalex.org/W2088940417","https://openalex.org/W2112861192","https://openalex.org/W2117842026","https://openalex.org/W2123164779","https://openalex.org/W2127020756","https://openalex.org/W2168014143"],"related_works":["https://openalex.org/W2131193457","https://openalex.org/W2952691602","https://openalex.org/W3209232490","https://openalex.org/W2070754243","https://openalex.org/W1585146582","https://openalex.org/W2207405255","https://openalex.org/W1974611425","https://openalex.org/W1973713130","https://openalex.org/W1530486604","https://openalex.org/W1984520810"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2],"basic":[3],"introduction":[4],"to":[5,19],"the":[6,20],"theories":[7],"of":[8,22],"M\u00f6bius":[9],"structures":[10],"and":[11,14],"hyperbolic":[12,26],"ends":[13],"we":[15],"study":[16],"their":[17],"applications":[18],"theory":[21],"$k$-surfaces":[23],"in":[24],"$3$-dimensional":[25],"space.":[27]},"counts_by_year":[],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
