{"id":"https://openalex.org/W7220965161","doi":"https://doi.org/10.48550/arxiv.2610.08885","title":"Quadratic differentials in Teichm\u00fcller theory and complex harmonic maps","display_name":"Quadratic differentials in Teichm\u00fcller theory and complex harmonic maps","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220965161","doi":"https://doi.org/10.48550/arxiv.2610.08885"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08885","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08885","pdf_url":"https://arxiv.org/pdf/2610.08885","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/2610.08885","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087394282","display_name":"Christian El Emam","orcid":"https://orcid.org/0000-0002-5622-8499","observed_orcids":["https://orcid.org/0000-0002-5622-8499"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emam, Christian El","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004797150","display_name":"Nathaniel Sagman","orcid":"https://orcid.org/0000-0002-8485-7073","observed_orcids":["https://orcid.org/0000-0002-8485-7073"]},"institutions":[{"id":"https://openalex.org/I55143463","display_name":"University of Turin","ror":"https://ror.org/048tbm396","country_code":"IT","type":"education","lineage":["https://openalex.org/I55143463"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Sagman, Nathaniel","raw_affiliation_strings":["Christian El Emam : University of Torino , Dipartimento di Matematica \"Giuseppe Peano\" , Via Carlo Alberto, 10 , 10123 Torino , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Christian El Emam : University of Torino , Dipartimento di Matematica \"Giuseppe Peano\" , Via Carlo Alberto, 10 , 10123 Torino , Italy","institution_ids":["https://openalex.org/I55143463"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.7631999850273132,"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":0.7631999850273132,"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/T12351","display_name":"Geometry and complex manifolds","score":0.1324000060558319,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.019700000062584877,"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/quadratic-differentials","display_name":"quadratic differentials","score":0.9869999885559082},{"id":"https://openalex.org/keywords/teichmuller-space","display_name":"Teichm\u00fcller space","score":0.9950000047683716},{"id":"https://openalex.org/keywords/bers-embedding","display_name":"Bers embedding","score":0.9980000257492065},{"id":"https://openalex.org/keywords/complex-projective-structures","display_name":"complex projective structures","score":0.9639999866485596}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7774999737739563},{"id":"https://openalex.org/C6270764","wikidata":"https://www.wikidata.org/wiki/Q5659257","display_name":"Harmonic map","level":2,"score":0.6930999755859375},{"id":"https://openalex.org/C32518243","wikidata":"https://www.wikidata.org/wiki/Q907926","display_name":"Holonomy","level":2,"score":0.6545000076293945},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6184999942779541},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5795000195503235},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.5600000023841858},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.45080000162124634},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4122999906539917},{"id":"https://openalex.org/C39292890","wikidata":"https://www.wikidata.org/wiki/Q864589","display_name":"Schwarzian derivative","level":2,"score":0.4034999907016754},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.38920000195503235},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.3887999951839447},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.37279999256134033},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.3359000086784363},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C53936288","wikidata":"https://www.wikidata.org/wiki/Q2634828","display_name":"Inverse limit","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C91066650","wikidata":"https://www.wikidata.org/wiki/Q2400539","display_name":"Teichm\u00fcller space","level":3,"score":0.27799999713897705},{"id":"https://openalex.org/C18556879","wikidata":"https://www.wikidata.org/wiki/Q753035","display_name":"Riemann surface","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.26649999618530273}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08885","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08885","pdf_url":"https://arxiv.org/pdf/2610.08885","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.2610.08885","doi":"https://doi.org/10.48550/arxiv.2610.08885","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08885","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.08885","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08885","pdf_url":"https://arxiv.org/pdf/2610.08885","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/W7220965161.pdf","grobid_xml":"https://content.openalex.org/works/W7220965161.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2364206260","https://openalex.org/W4415069420","https://openalex.org/W2746649903","https://openalex.org/W4226184307","https://openalex.org/W1035519881","https://openalex.org/W4226515735","https://openalex.org/W4413478134","https://openalex.org/W2079516137","https://openalex.org/W2385924033","https://openalex.org/W3165132091"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"Hitchin-Wolf's":[3],"harmonic":[4,49,61,81],"map":[5,18,28,35],"parametrization":[6],"of":[7,23,45,66,69,79,109,125],"Teichm\u00fcller":[8],"space,":[9,47],"the":[10,30,53,64,72,77,87,91,115],"Schwarzian":[11],"holonomy":[12,17],"map,":[13],"and":[14,90,120],"Uhlenbeck's":[15],"almost-Fuchsian":[16],"all":[19],"arise":[20],"as":[21],"restrictions":[22],"a":[24,37,84,105,123],"single":[25],"locally":[26],"biholomorphic":[27],"into":[29],"$\\mathrm{PSL}(2,\\mathbb{C})$":[31],"character":[32],"variety.":[33],"The":[34,56],"admits":[36],"right":[38],"inverse":[39],"defined":[40],"on":[41,86],"an":[42,100],"open":[43],"subset":[44],"quasi-Fuchsian":[46],"encoding":[48],"maps":[50,62],"together":[51],"with":[52,83],"Bers":[54],"embedding.":[55],"construction":[57],"goes":[58],"through":[59],"complex":[60,80,94],"to":[63,93,99],"space":[65,119],"oriented":[67],"geodesics":[68],"$\\mathbb{H}^3$.":[70],"Along":[71],"way,":[73],"we":[74,103,121],"further":[75],"develop":[76],"theory":[78],"maps,":[82],"focus":[85],"natural":[88],"$\\mathbb{C}^*$-action":[89],"relation":[92],"projective":[95],"structures.":[96],"This":[97],"leads":[98],"independent":[101],"application:":[102],"obtain":[104],"new":[106],"geometric":[107],"interpretation":[108],"certain":[110],"real":[111],"twistor":[112],"lines":[113],"in":[114],"rank-two":[116],"Deligne-Hitchin":[117],"moduli":[118],"recover":[122],"theorem":[124],"Gothen-Silva.":[126]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}