{"id":"https://openalex.org/W7212064231","doi":"https://doi.org/10.48550/arxiv.2609.05715","title":"Interface foliation near a minimal isoparametric hypersurface for the Allen-Cahn equation","display_name":"Interface foliation near a minimal isoparametric hypersurface for the Allen-Cahn equation","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7212064231","doi":"https://doi.org/10.48550/arxiv.2609.05715"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.05715","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05715","pdf_url":"https://arxiv.org/pdf/2609.05715","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/2609.05715","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020868858","display_name":"Guillermo Sebasti\u00e1n Henry","orcid":"https://orcid.org/0009-0003-2568-1834","observed_orcids":["https://orcid.org/0009-0003-2568-1834"]},"institutions":[{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"government","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I24354313","display_name":"Universidad de Buenos Aires","ror":"https://ror.org/0081fs513","country_code":"AR","type":"education","lineage":["https://openalex.org/I24354313"]},{"id":"https://openalex.org/I4210144290","display_name":"Institute of Astronomy and Space Physics","ror":"https://ror.org/03rq94151","country_code":"AR","type":"facility","lineage":["https://openalex.org/I151201029","https://openalex.org/I24354313","https://openalex.org/I4210123736","https://openalex.org/I4210144290","https://openalex.org/I4387155568"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Henry, Guillermo","raw_affiliation_strings":["Departamento de Matem\u00e1tica , FCEyN , Universidad de BuenosAires and IMAS , CONICET-UBA , Ciu- dad Universitaria , Pab. I. , C1428EHA , Buenos Aires , Argentina and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica , FCEyN , Universidad de BuenosAires and IMAS , CONICET-UBA , Ciu- dad Universitaria , Pab. I. , C1428EHA , Buenos Aires , Argentina and","institution_ids":["https://openalex.org/I151201029","https://openalex.org/I24354313","https://openalex.org/I4210144290"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062713974","display_name":"Jimmy Petean","orcid":"https://orcid.org/0000-0002-6750-9472","observed_orcids":["https://orcid.org/0000-0002-6750-9472"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Petean, Jimmy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.8690999746322632,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.8690999746322632,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.12540000677108765,"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":0.00039999998989515007,"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/allen-cahn-equation","display_name":"Allen-Cahn equation","score":0.9940000176429749},{"id":"https://openalex.org/keywords/isoparametric-hypersurfaces","display_name":"isoparametric hypersurfaces","score":0.8930000066757202},{"id":"https://openalex.org/keywords/minimal-hypersurfaces","display_name":"minimal hypersurfaces","score":0.906000018119812},{"id":"https://openalex.org/keywords/sign-changing-solutions","display_name":"sign-changing solutions","score":0.8550000190734863},{"id":"https://openalex.org/keywords/level-sets","display_name":"level sets","score":0.6710000038146973},{"id":"https://openalex.org/keywords/positive-ricci-curvature","display_name":"positive Ricci curvature","score":0.8849999904632568},{"id":"https://openalex.org/keywords/energy-bounds","display_name":"energy bounds","score":0.4620000123977661},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.36800000071525574}],"concepts":[{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.9021999835968018},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.800000011920929},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6650999784469604},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.578000009059906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5314000248908997},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5310999751091003},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5015000104904175},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4244999885559082},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4235999882221222},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.3961000144481659},{"id":"https://openalex.org/C168425004","wikidata":"https://www.wikidata.org/wiki/Q525802","display_name":"Foliation (geology)","level":3,"score":0.39250001311302185},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37459999322891235},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.36550000309944153},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.323199987411499},{"id":"https://openalex.org/C153008295","wikidata":"https://www.wikidata.org/wiki/Q6535093","display_name":"Level set (data structures)","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.31299999356269836},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C30707913","wikidata":"https://www.wikidata.org/wiki/Q1545397","display_name":"Minimal surface","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C167204820","wikidata":"https://www.wikidata.org/wiki/Q912058","display_name":"Simply connected space","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26350000500679016},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.259799987077713},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.25760000944137573},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.05715","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05715","pdf_url":"https://arxiv.org/pdf/2609.05715","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.2609.05715","doi":"https://doi.org/10.48550/arxiv.2609.05715","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.05715","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:2609.05715","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05715","pdf_url":"https://arxiv.org/pdf/2609.05715","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212064231.pdf","grobid_xml":"https://content.openalex.org/works/W7212064231.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2995028916","https://openalex.org/W7170536684"],"related_works":["https://openalex.org/W2949390354","https://openalex.org/W2101042449","https://openalex.org/W7221199514","https://openalex.org/W2159456902","https://openalex.org/W2963134212","https://openalex.org/W4385848472","https://openalex.org/W2952096840","https://openalex.org/W2509961155","https://openalex.org/W2921071766","https://openalex.org/W2038059270"],"abstract_inverted_index":{"Let":[0,11],"$(M,g)$":[1],"be":[2,13],"a":[3,14,30,44],"closed":[4],"Riemannian":[5],"manifold":[6],"of":[7,26,46,63],"positive":[8,35],"Ricci":[9],"curvature.":[10],"$f$":[12,27,64],"proper":[15],"isoparametric":[16,80],"function":[17],"on":[18],"$M$,":[19],"and":[20,38,65,86],"$\u0393$":[21,82],"the":[22,47,60,74,78,87],"unique":[23],"level":[24,61],"set":[25],"which":[28,56],"is":[29,57,89],"minimal":[31,79],"hypersurface.":[32],"For":[33],"any":[34],"integer":[36],"$k$,":[37],"$\u03bb>0$":[39],"large":[40],"enough,":[41],"we":[42],"construct":[43],"solution":[45],"Allen-Cahn":[48],"equation":[49],"$":[50],"\u0394u":[51],"+":[52],"\u03bb(u-u^3":[53],")":[54],"=0$":[55],"constant":[58],"along":[59],"sets":[62],"has":[66],"exactly":[67],"$k$":[68],"nodal":[69,75],"components.":[70],"We":[71],"prove":[72],"that":[73],"components":[76],"approach":[77],"hypersurface":[81],"as":[83],"$\u03bb\\rightarrow":[84],"\\infty$":[85],"energy":[88],"uniformly":[90],"bounded":[91],"for":[92],"all":[93],"such":[94],"solutions.":[95]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}
