{"id":"https://openalex.org/W7213606202","doi":"https://doi.org/10.48550/arxiv.2609.20042","title":"Non-simple blow-up for the Chern--Simons--Higgs equation on Riemannian surfaces","display_name":"Non-simple blow-up for the Chern--Simons--Higgs equation on Riemannian surfaces","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213606202","doi":"https://doi.org/10.48550/arxiv.2609.20042"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20042","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20042","pdf_url":"https://arxiv.org/pdf/2609.20042","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/2609.20042","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047363697","display_name":"Youngae Lee","orcid":"https://orcid.org/0000-0002-7403-2334","observed_orcids":["https://orcid.org/0000-0002-7403-2334"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee, Youngae","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5152140003","display_name":"Lei Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Lei","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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9603999853134155,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9603999853134155,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.023800000548362732,"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"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.012600000016391277,"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/vortex-solutions","display_name":"vortex solutions","score":0.4230000078678131},{"id":"https://openalex.org/keywords/magnetic-flux-concentration","display_name":"magnetic flux concentration","score":0.8830000162124634},{"id":"https://openalex.org/keywords/flat-torus","display_name":"flat torus","score":0.8769999742507935},{"id":"https://openalex.org/keywords/mean-field-regime","display_name":"mean-field regime","score":0.7429999709129333},{"id":"https://openalex.org/keywords/cluster-mass","display_name":"cluster mass","score":0.4860000014305115}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7361000180244446},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.6444000005722046},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6284999847412109},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5874999761581421},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5665000081062317},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.5522000193595886},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4950000047683716},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4853000044822693},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.4708999991416931},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4472000002861023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44209998846054077},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.413100004196167},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.32989999651908875},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28619998693466187},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.2574000060558319}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20042","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20042","pdf_url":"https://arxiv.org/pdf/2609.20042","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.2609.20042","doi":"https://doi.org/10.48550/arxiv.2609.20042","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20042","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.20042","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20042","pdf_url":"https://arxiv.org/pdf/2609.20042","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/F4320319003","display_name":"\u0110\u1ea1i h\u1ecdc Kinh t\u1ebf Th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh","ror":"https://ror.org/010yce376"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213606202.pdf","grobid_xml":"https://content.openalex.org/works/W7213606202.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1983558565","https://openalex.org/W1992445470","https://openalex.org/W1995177535","https://openalex.org/W2013216031","https://openalex.org/W2056182538","https://openalex.org/W2058154782","https://openalex.org/W2080861267","https://openalex.org/W2090618980","https://openalex.org/W2094795708","https://openalex.org/W2096854993","https://openalex.org/W2102664470","https://openalex.org/W2491725655","https://openalex.org/W2543637670","https://openalex.org/W2566027724","https://openalex.org/W2893750230","https://openalex.org/W3124386058","https://openalex.org/W3153765571","https://openalex.org/W4392250588","https://openalex.org/W4392557866","https://openalex.org/W4396929757","https://openalex.org/W7133773039","https://openalex.org/W7214711089"],"related_works":["https://openalex.org/W2056182538","https://openalex.org/W2543637670","https://openalex.org/W7223055130","https://openalex.org/W7167091681","https://openalex.org/W7214711089","https://openalex.org/W3028270207","https://openalex.org/W4379924886","https://openalex.org/W2060561848","https://openalex.org/W1995177535","https://openalex.org/W2094795708"],"abstract_inverted_index":{"The":[0],"existence":[1,49],"and":[2,70,91,108,152],"structure":[3],"of":[4,50,78,104],"non-simple":[5,51,80,116,136],"blow-up":[6,52,117,138,156],"are":[7,27],"fundamental":[8],"questions":[9],"for":[10,44,134],"the":[11,37,48,55,67,76,165],"self-dual":[12],"Chern--Simons--Higgs":[13,57],"equation.":[14],"Physically,":[15],"this":[16],"phenomenon":[17],"describes":[18],"magnetic-flux":[19],"concentration":[20],"in":[21,65,123,164],"several":[22],"cores":[23,35,77],"whose":[24],"mutual":[25],"distances":[26],"much":[28],"larger":[29],"than":[30],"their":[31],"widths,":[32],"although":[33],"all":[34],"approach":[36],"same":[38],"vortex":[39,155],"point.":[40],"Despite":[41],"substantial":[42],"progress":[43],"singular":[45],"Liouville":[46],"equations,":[47],"solutions":[53,118],"to":[54],"full":[56],"equation":[58],"on":[59,119,139],"closed":[60,120],"surfaces":[61,122],"has":[62],"remained":[63],"open":[64],"both":[66,124],"Chern--Simons":[68],"(CS)":[69],"mean-field":[71],"regimes.":[72,125],"We":[73,113],"prove":[74],"that":[75,154],"every":[79],"cluster":[81,106],"have":[82],"equal":[83],"limiting":[84],"masses,":[85],"share":[86],"a":[87,109,130,145],"common":[88],"profile":[89],"type,":[90],"form":[92],"an":[93,100],"asymptotically":[94],"regular":[95],"polygon.":[96],"These":[97],"identities":[98],"yield":[99],"explicit":[101],"finite":[102],"list":[103],"admissible":[105],"masses":[107],"four-unit":[110],"mass-gap":[111],"criterion.":[112],"also":[114],"construct":[115],"Riemannian":[121],"Together,":[126],"these":[127],"results":[128],"establish":[129],"sharp":[131],"arithmetic":[132],"criterion":[133],"single-point":[135],"CS":[137],"each":[140],"fixed":[141],"flat":[142],"torus":[143],"when":[144],"suitable":[146],"exterior":[147],"divisor":[148],"may":[149],"be":[150,159],"chosen,":[151],"show":[153],"need":[157],"not":[158],"simple,":[160],"answering":[161],"Li--Liu's":[162],"question":[163],"negative.":[166]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-19T00:00:00"}