{"id":"https://openalex.org/W7214048635","doi":"https://doi.org/10.48550/arxiv.2609.24451","title":"Geometric flows of branched transportation networks","display_name":"Geometric flows of branched transportation networks","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214048635","doi":"https://doi.org/10.48550/arxiv.2609.24451"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.24451","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24451","pdf_url":"https://arxiv.org/pdf/2609.24451","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/2609.24451","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041694403","display_name":"Julius Lohmann","orcid":"https://orcid.org/0000-0002-4359-9346","observed_orcids":["https://orcid.org/0000-0002-4359-9346"]},"institutions":[{"id":"https://openalex.org/I205924995","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466","country_code":"JP","type":"nonprofit","lineage":["https://openalex.org/I1319490839","https://openalex.org/I205924995"]},{"id":"https://openalex.org/I4400009020","display_name":"Institute of Science Tokyo","ror":"https://ror.org/05dqf9946","country_code":"JP","type":"education","lineage":["https://openalex.org/I4400009020"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Lohmann, Julius","raw_affiliation_strings":["Department of Mathematics , Institute of Science Tokyo","International Research Fellow of Japan Society for the Promotion of Science , lohmann"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Institute of Science Tokyo","institution_ids":["https://openalex.org/I4400009020"]},{"raw_affiliation_string":"International Research Fellow of Japan Society for the Promotion of Science , lohmann","institution_ids":["https://openalex.org/I205924995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053599979","display_name":"Yoshihiro Tonegawa","orcid":"https://orcid.org/0000-0003-1552-3608","observed_orcids":["https://orcid.org/0000-0003-1552-3608"]},"institutions":[{"id":"https://openalex.org/I4400009020","display_name":"Institute of Science Tokyo","ror":"https://ror.org/05dqf9946","country_code":"JP","type":"education","lineage":["https://openalex.org/I4400009020"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tonegawa, Yoshihiro","raw_affiliation_strings":["Department of Mathematics , Institute of Science Tokyo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Institute of Science Tokyo","institution_ids":["https://openalex.org/I4400009020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":1.0,"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":1.0,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.0,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0,"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/geometric-flows","display_name":"geometric flows","score":0.8539999723434448},{"id":"https://openalex.org/keywords/brakke-flow","display_name":"Brakke flow","score":0.8970000147819519},{"id":"https://openalex.org/keywords/nonconvex-variational-problems","display_name":"nonconvex variational problems","score":0.7170000076293945},{"id":"https://openalex.org/keywords/surface-singularities","display_name":"singular surfaces","score":0.6740000247955322},{"id":"https://openalex.org/keywords/mass-transfer","display_name":"mass transfer","score":0.3440000116825104}],"concepts":[{"id":"https://openalex.org/C19220575","wikidata":"https://www.wikidata.org/wiki/Q1934099","display_name":"Subadditivity","level":2,"score":0.8475000262260437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7354000210762024},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5540000200271606},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.49799999594688416},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.49059998989105225},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.47099998593330383},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.45419999957084656},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4404999911785126},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.43130001425743103},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3813999891281128},{"id":"https://openalex.org/C2993719964","wikidata":"https://www.wikidata.org/wiki/Q178512","display_name":"Mass transportation","level":3,"score":0.33009999990463257},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.3203999996185303},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31949999928474426},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.30250000953674316},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3019999861717224},{"id":"https://openalex.org/C2989209122","wikidata":"https://www.wikidata.org/wiki/Q178512","display_name":"Mass transport","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C32209215","wikidata":"https://www.wikidata.org/wiki/Q5535483","display_name":"Geometric flow","level":3,"score":0.2962999939918518},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2784999907016754},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C49777392","wikidata":"https://www.wikidata.org/wiki/Q5535495","display_name":"Geometric networks","level":3,"score":0.2551000118255615},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.24451","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24451","pdf_url":"https://arxiv.org/pdf/2609.24451","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.2609.24451","doi":"https://doi.org/10.48550/arxiv.2609.24451","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.24451","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:2609.24451","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24451","pdf_url":"https://arxiv.org/pdf/2609.24451","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/G7383225088","display_name":"Canonical mean curvature flow and its application to evolution problems","funder_award_id":"23H00085","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214048635.pdf","grobid_xml":"https://content.openalex.org/works/W7214048635.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W160928081","https://openalex.org/W1967790603","https://openalex.org/W2024004913","https://openalex.org/W2028258142","https://openalex.org/W2050551798","https://openalex.org/W2082053483","https://openalex.org/W2082252207","https://openalex.org/W2084952261","https://openalex.org/W2155280009","https://openalex.org/W2237119880","https://openalex.org/W2241589958","https://openalex.org/W2516111629","https://openalex.org/W2594151313","https://openalex.org/W2611808105","https://openalex.org/W2777142600","https://openalex.org/W2884005814","https://openalex.org/W2964694134","https://openalex.org/W2992577177","https://openalex.org/W3199960938","https://openalex.org/W4415022729"],"related_works":["https://openalex.org/W2611808105","https://openalex.org/W3199960938","https://openalex.org/W2964110112","https://openalex.org/W2168383320","https://openalex.org/W618245743","https://openalex.org/W2901079785","https://openalex.org/W4300956799","https://openalex.org/W2760612516","https://openalex.org/W7096980206","https://openalex.org/W2933423222"],"abstract_inverted_index":{"The":[0,20,50],"branched":[1,133,157],"transport":[2,134,158],"problem":[3,11],"is":[4,22,122],"a":[5,85,95,119,144,166],"nonconvex":[6],"and":[7,30,131,160],"nonsmooth":[8],"variational":[9,111],"optimization":[10],"on":[12],"normal":[13,104],"$1$-currents":[14],"in":[15,58,80],"$\\mathbb{R}^n$":[16],"with":[17,23,34,125,165],"prescribed":[18],"boundary.":[19],"optimality":[21],"respect":[24,126],"to":[25,40,53,68,73,103,127,170],"some":[26],"non-decreasing,":[27],"lower":[28],"semicontinuous,":[29],"subadditive":[31],"function":[32],"$\u03c4:\\mathbb{R}_+\\to\\mathbb{R}_+$":[33],"$\u03c4(0)=0$":[35],"describing":[36],"the":[37,59,76,81,89,116,128,138,156],"cost":[38,135],"$\u03c4(m)$":[39],"move":[41],"an":[42],"amount":[43],"of":[44,61,75,88,98,118],"mass":[45],"$m$":[46],"per":[47],"unit":[48],"distance.":[49],"subadditivity":[51],"leads":[52],"complicated,":[54],"hierarchically":[55],"ramified":[56],"patterns":[57],"support":[60],"(suboptimal)":[62],"solutions.":[63],"These":[64],"network-like":[65],"sets":[66],"appear":[67],"have":[69],"regularity":[70],"properties":[71],"similar":[72],"those":[74],"singular":[77],"surfaces":[78],"arising":[79],"so-called":[82],"Brakke":[83],"flow,":[84],"weak":[86],"generalization":[87],"mean":[90],"curvature":[91],"flow.":[92],"We":[93,114,141],"construct":[94],"geometric":[96,139,147],"flow":[97,148],"transportation":[99],"networks,":[100],"which":[101],"correspond":[102],"real":[105],"$1$-rectifiable":[106],"currents,":[107],"by":[108,150],"modifying":[109],"Brakke's":[110,171],"approximation":[112],"scheme.":[113],"prove":[115],"existence":[117],"limit":[120],"that":[121],"H\u00f6lder":[123],"continuous":[124],"flat":[129],"norm":[130],"whose":[132,152],"decreases":[136],"along":[137],"evolution.":[140],"further":[142],"analyze":[143],"closely":[145],"related":[146],"approximated":[149],"$1$-varifolds,":[151],"weight":[153],"measures":[154],"model":[155],"cost,":[159],"establish":[161],"its":[162],"$1$-rectifiability":[163],"together":[164],"motion":[167],"law":[168],"analogous":[169],"inequality.":[172]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}