{"id":"https://openalex.org/W7203650996","doi":"https://doi.org/10.48550/arxiv.2608.13927","title":"Transversal H\u00f6lder Criteria and Dini--Zygmund Endpoint Regularity for Hyperbolic Harmonic Mappings","display_name":"Transversal H\u00f6lder Criteria and Dini--Zygmund Endpoint Regularity for Hyperbolic Harmonic Mappings","publication_year":2026,"publication_date":"2026-08-14","ids":{"openalex":"https://openalex.org/W7203650996","doi":"https://doi.org/10.48550/arxiv.2608.13927"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.13927","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13927","pdf_url":"https://arxiv.org/pdf/2608.13927","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/2608.13927","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147340036","display_name":"Suling Tan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tan, Suling","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101999315","display_name":"Hongping Li","orcid":"https://orcid.org/0000-0001-5149-5339","observed_orcids":["https://orcid.org/0000-0001-5149-5339"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Hong-Ping","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":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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.8935999870300293,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.8935999870300293,"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/T11822","display_name":"Analytic and geometric function theory","score":0.07509999722242355,"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":0.004000000189989805,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/real-hyperbolic-space","display_name":"real hyperbolic space","score":0.8370000123977661},{"id":"https://openalex.org/keywords/holder-continuity","display_name":"H\u00f6lder continuity","score":0.9110000133514404},{"id":"https://openalex.org/keywords/besov-spaces","display_name":"Besov spaces","score":0.7580000162124634},{"id":"https://openalex.org/keywords/vertical-lines","display_name":"vertical lines","score":0.5669999718666077},{"id":"https://openalex.org/keywords/upper-half-space","display_name":"upper half-space","score":0.6110000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.84170001745224},{"id":"https://openalex.org/C145050668","wikidata":"https://www.wikidata.org/wiki/Q165301","display_name":"Hyperbola","level":2,"score":0.7067000269889832},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6151999831199646},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.598800003528595},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.588699996471405},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5515000224113464},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.47040000557899475},{"id":"https://openalex.org/C163016742","wikidata":"https://www.wikidata.org/wiki/Q640600","display_name":"Inverse hyperbolic function","level":4,"score":0.4700999855995178},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.4327000081539154},{"id":"https://openalex.org/C3098717","wikidata":"https://www.wikidata.org/wiki/Q1144872","display_name":"Modulus of continuity","level":3,"score":0.4269999861717224},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.42289999127388},{"id":"https://openalex.org/C8077415","wikidata":"https://www.wikidata.org/wiki/Q2596534","display_name":"Poisson kernel","level":2,"score":0.38960000872612},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.38600000739097595},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.3783000111579895},{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C55862258","wikidata":"https://www.wikidata.org/wiki/Q1017238","display_name":"Hyperbolic coordinates","level":5,"score":0.3449999988079071},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.33959999680519104},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C51691630","wikidata":"https://www.wikidata.org/wiki/Q3925833","display_name":"Hyperbolic equilibrium point","level":4,"score":0.33399999141693115},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C82673646","wikidata":"https://www.wikidata.org/wiki/Q2246553","display_name":"Hyperbolic triangle","level":4,"score":0.3183000087738037},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C63356602","wikidata":"https://www.wikidata.org/wiki/Q1986013","display_name":"Lacunary function","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C97654310","wikidata":"https://www.wikidata.org/wiki/Q574023","display_name":"Hyperbolic tree","level":4,"score":0.2800999879837036},{"id":"https://openalex.org/C120362076","wikidata":"https://www.wikidata.org/wiki/Q1149336","display_name":"Trigonometric series","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26750001311302185},{"id":"https://openalex.org/C39308205","wikidata":"https://www.wikidata.org/wiki/Q7880612","display_name":"Ultraparallel theorem","level":5,"score":0.2651999890804291},{"id":"https://openalex.org/C46581059","wikidata":"https://www.wikidata.org/wiki/Q116301","display_name":"Periodic point","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.2596000134944916},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C155940","wikidata":"https://www.wikidata.org/wiki/Q7886967","display_name":"Uniqueness theorem for Poisson's equation","level":3,"score":0.25699999928474426},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C39269415","wikidata":"https://www.wikidata.org/wiki/Q796341","display_name":"Bounded mean oscillation","level":3,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.13927","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13927","pdf_url":"https://arxiv.org/pdf/2608.13927","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.2608.13927","doi":"https://doi.org/10.48550/arxiv.2608.13927","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.13927","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:2608.13927","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13927","pdf_url":"https://arxiv.org/pdf/2608.13927","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":[{"id":"https://openalex.org/G260096214","display_name":null,"funder_award_id":"12271189","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203650996.pdf","grobid_xml":"https://content.openalex.org/works/W7203650996.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1547021768","https://openalex.org/W2951575129","https://openalex.org/W4391017388","https://openalex.org/W4406775323","https://openalex.org/W4407149049"],"related_works":["https://openalex.org/W4406775323","https://openalex.org/W2327451300","https://openalex.org/W2952158301","https://openalex.org/W3009525354","https://openalex.org/W3148266794","https://openalex.org/W3169003605","https://openalex.org/W3152637756","https://openalex.org/W2963939626","https://openalex.org/W4287921636","https://openalex.org/W4281735719"],"abstract_inverted_index":{"Let":[0],"$n\\ge3$,":[1],"and":[2,26,62],"let":[3],"$u$":[4],"be":[5],"a":[6],"bounded":[7],"hyperbolic":[8,14],"harmonic":[9],"mapping":[10],"on":[11,66],"the":[12,30,57,67,72],"real":[13],"upper":[15],"half-space":[16],"$\\mathbb":[17],"H^n$.":[18],"First,":[19],"for":[20,29],"$0<\u03b1<1$,":[21],"we":[22,37,55],"establish":[23],"quantitative":[24],"transversal":[25],"modulus":[27],"criteria":[28,45],"global":[31,59],"$\u03b1$-H\u00f6lder":[32],"continuity":[33,61],"of":[34],"$u$.":[35],"Then,":[36],"construct":[38],"lacunary":[39],"examples":[40],"to":[41],"show":[42],"that":[43,70],"these":[44],"are":[46],"invalid":[47],"when":[48],"$\u03b1=1$.":[49],"Finally,":[50],"under":[51],"additional":[52],"integral":[53],"conditions,":[54],"obtain":[56],"corresponding":[58],"Lipschitz":[60,73],"give":[63],"Dini--Zygmund":[64],"conditions":[65],"boundary":[68],"trace":[69],"ensure":[71],"continuity.":[74]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-18T00:00:00"}
