{"id":"https://openalex.org/W7204917779","doi":"https://doi.org/10.48550/arxiv.2608.30752","title":"Quasi-convexity of energy functions along Teichm\u00fcller geodesics","display_name":"Quasi-convexity of energy functions along Teichm\u00fcller geodesics","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204917779","doi":"https://doi.org/10.48550/arxiv.2608.30752"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30752","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30752","pdf_url":"https://arxiv.org/pdf/2608.30752","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/2608.30752","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151851438","display_name":"Inkang Kim","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I50632499","display_name":"Chongqing University of Technology","ror":"https://ror.org/04vgbd477","country_code":"CN","type":"education","lineage":["https://openalex.org/I50632499"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kim, Inkang","raw_affiliation_strings":["Mathematical Science Research Center , Chongqing University of Technol- ogy , Chongqing 400054 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Science Research Center , Chongqing University of Technol- ogy , Chongqing 400054 , China","institution_ids":["https://openalex.org/I50632499"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037660606","display_name":"Xueyuan Wan","orcid":"https://orcid.org/0000-0003-2530-5583","observed_orcids":["https://orcid.org/0000-0003-2530-5583"]},"institutions":[{"id":"https://openalex.org/I50632499","display_name":"Chongqing University of Technology","ror":"https://ror.org/04vgbd477","country_code":"CN","type":"education","lineage":["https://openalex.org/I50632499"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wan, Xueyuan","raw_affiliation_strings":["Mathematical Science Research Center , Chongqing University of Technol- ogy , Chongqing 400054 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Science Research Center , Chongqing University of Technol- ogy , Chongqing 400054 , China","institution_ids":["https://openalex.org/I50632499"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010993390","display_name":"Genkai Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I50632499","display_name":"Chongqing University of Technology","ror":"https://ror.org/04vgbd477","country_code":"CN","type":"education","lineage":["https://openalex.org/I50632499"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Genkai","raw_affiliation_strings":["Mathematical Science Research Center , Chongqing University of Technol- ogy , Chongqing 400054 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Science Research Center , Chongqing University of Technol- ogy , Chongqing 400054 , China","institution_ids":["https://openalex.org/I50632499"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I50632499"],"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":0.8916000127792358,"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":0.8916000127792358,"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":0.05220000073313713,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.031599998474121094,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/teichmuller-space","display_name":"Teichm\u00fcller space","score":0.8840000033378601},{"id":"https://openalex.org/keywords/teichmuller-geodesics","display_name":"Teichm\u00fcller geodesics","score":0.9879999756813049},{"id":"https://openalex.org/keywords/quasiconvexity","display_name":"quasiconvexity","score":0.921999990940094},{"id":"https://openalex.org/keywords/energy-function","display_name":"energy function","score":0.8330000042915344},{"id":"https://openalex.org/keywords/harmonic-maps","display_name":"harmonic maps","score":0.9909999966621399},{"id":"https://openalex.org/keywords/asymptotic-growth","display_name":"asymptotic growth","score":0.6850000023841858},{"id":"https://openalex.org/keywords/covering-spaces","display_name":"covering spaces","score":0.7429999709129333},{"id":"https://openalex.org/keywords/hyperbolic-surfaces","display_name":"hyperbolic surfaces","score":0.8429999947547913}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.887499988079071},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6772000193595886},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6230999827384949},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.583899974822998},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5392000079154968},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5116000175476074},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.44830000400543213},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.3824000060558319},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.3368000090122223},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.3158000111579895},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C51691630","wikidata":"https://www.wikidata.org/wiki/Q3925833","display_name":"Hyperbolic equilibrium point","level":4,"score":0.29490000009536743},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29249998927116394},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26980000734329224},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.26420000195503235}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30752","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30752","pdf_url":"https://arxiv.org/pdf/2608.30752","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.2608.30752","doi":"https://doi.org/10.48550/arxiv.2608.30752","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30752","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:2608.30752","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30752","pdf_url":"https://arxiv.org/pdf/2608.30752","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":[{"id":"https://openalex.org/F4320329205","display_name":"Banff International Research Station for Mathematical Innovation and Discovery","ror":"https://ror.org/00ehdct47"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204917779.pdf","grobid_xml":"https://content.openalex.org/works/W7204917779.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4416157474"],"related_works":["https://openalex.org/W4214829638","https://openalex.org/W7103391019","https://openalex.org/W2891247249","https://openalex.org/W2981726864","https://openalex.org/W1833362527","https://openalex.org/W2952792096","https://openalex.org/W4388767689","https://openalex.org/W3101549775","https://openalex.org/W7010087257","https://openalex.org/W2187978108"],"abstract_inverted_index":{"Hyperbolic":[0],"length":[1,48,82],"functions":[2,29,124],"are":[3,14],"among":[4],"the":[5,24,47,61,81,85,94,100,131],"most":[6],"fundamental":[7],"ones":[8],"on":[9,77],"Teichm\u00fcller":[10,17,66,86,126],"space,":[11],"and":[12,43,54,112,118,128],"they":[13],"quasi-convex":[15,64],"along":[16,65,84,125],"geodesics.":[18],"In":[19],"this":[20],"paper,":[21],"we":[22,59,73],"investigate":[23],"same":[25],"question":[26],"for":[27,102],"energy":[28,62,95,123],"of":[30,46,80,122],"harmonic":[31],"maps":[32,104],"in":[33],"two":[34],"natural":[35,132],"settings,":[36],"which":[37],"may":[38],"be":[39],"viewed":[40],"as":[41],"nonlinear":[42],"higher-dimensional":[44],"analogs":[45],"functions.":[49,96],"For":[50],"a":[51,55,69,90],"fixed":[52,110],"domain":[53],"varying":[56,113],"hyperbolic":[57,107],"target,":[58],"prove":[60,99],"is":[63,135],"geodesics":[67,127],"under":[68],"filling":[70],"hypothesis.":[71],"Furthermore,":[72],"generalize":[74],"Masur's":[75],"result":[76],"asymptotic":[78],"growth":[79],"function":[83],"geodesic":[87],"determined":[88],"by":[89],"Jenkins-Strebel":[91],"differential":[92],"to":[93],"We":[97,115],"also":[98],"quasi-convexity":[101,136],"covering":[103],"between":[105],"closed":[106],"surfaces":[108],"with":[109],"target":[111],"domains.":[114],"derive":[116],"first":[117],"second":[119],"variation":[120],"formulas":[121],"explain":[129],"why":[130],"global":[133],"statement":[134],"rather":[137],"than":[138],"genuine":[139],"convexity.":[140]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}