{"id":"https://openalex.org/W7206197652","doi":"https://doi.org/10.48550/arxiv.2609.00108","title":"The double sphere solution in the liquid drop model","display_name":"The double sphere solution in the liquid drop model","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7206197652","doi":"https://doi.org/10.48550/arxiv.2609.00108"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.00108","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00108","pdf_url":"https://arxiv.org/pdf/2609.00108","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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/2609.00108","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139192059","display_name":"Manuel del Pino","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"del Pino, Manuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016122295","display_name":"Rupert L. Frank","orcid":"https://orcid.org/0000-0001-7973-4688","observed_orcids":["https://orcid.org/0000-0001-7973-4688"]},"institutions":[{"id":"https://openalex.org/I4210142743","display_name":"Munich Center for Quantum Science and Technology","ror":"https://ror.org/04xrcta15","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210142743","https://openalex.org/I8204097"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frank, Rupert L.","raw_affiliation_strings":["Mathematics Institute , University of Munich , Theresienstr. 39 , 80333 Munich , Germany, and","Munich Center for Quantum Science and Technology , Schellingstr. 4 , 80799 Munich , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Institute , University of Munich , Theresienstr. 39 , 80333 Munich , Germany, and","institution_ids":["https://openalex.org/I8204097"]},{"raw_affiliation_string":"Munich Center for Quantum Science and Technology , Schellingstr. 4 , 80799 Munich , Germany","institution_ids":["https://openalex.org/I4210142743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5139150179","display_name":"Monica Musso","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Musso, Monica","raw_affiliation_strings":["Department of Mathematical Sciences University of Bath , Bath BA2 7AY , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences University of Bath , Bath BA2 7AY , United Kingdom","institution_ids":["https://openalex.org/I51601045"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":0.9872999787330627,"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":0.9872999787330627,"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":0.008899999782443047,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/liquid-drop-model","display_name":"liquid drop model","score":0.890999972820282},{"id":"https://openalex.org/keywords/critical-domains","display_name":"critical domains","score":0.8399999737739563},{"id":"https://openalex.org/keywords/energy-functional","display_name":"energy functional","score":0.5049999952316284},{"id":"https://openalex.org/keywords/volume-constraint","display_name":"volume constraint","score":0.8519999980926514}],"concepts":[{"id":"https://openalex.org/C35377427","wikidata":"https://www.wikidata.org/wiki/Q3886264","display_name":"Axial symmetry","level":2,"score":0.5742999911308289},{"id":"https://openalex.org/C2781345722","wikidata":"https://www.wikidata.org/wiki/Q5308388","display_name":"Drop (telecommunication)","level":2,"score":0.5325000286102295},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.5145999789237976},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48100000619888306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47850000858306885},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4717000126838684},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.40639999508857727},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33169999718666077},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3292999863624573},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29019999504089355},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.2802000045776367},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.26170000433921814}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.00108","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00108","pdf_url":"https://arxiv.org/pdf/2609.00108","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.00108","doi":"https://doi.org/10.48550/arxiv.2609.00108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.00108","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.00108","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.00108","pdf_url":"https://arxiv.org/pdf/2609.00108","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7206197652.pdf","grobid_xml":"https://content.openalex.org/works/W7206197652.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7155196613","https://openalex.org/W7202341642"],"related_works":["https://openalex.org/W2962803217","https://openalex.org/W2951905381","https://openalex.org/W6884548576","https://openalex.org/W7047556829","https://openalex.org/W1491167723","https://openalex.org/W7203875634","https://openalex.org/W4299477358","https://openalex.org/W2009701727","https://openalex.org/W3213645259","https://openalex.org/W7155196613"],"abstract_inverted_index":{"We":[0,33,45],"consider":[1],"the":[2,11,29,59,78],"problem":[3],"of":[4,61,77],"finding":[5],"critical":[6],"domains":[7],"$\u03a9\\subset{\\mathbb":[8],"R}^3$":[9],"for":[10,35,53],"energy":[12],"functional":[13],"$$":[14,27],"\\mathcal":[15],"E":[16],"(\u03a9)":[17],"=":[18],"{\\rm":[19],"Per}\\,(\u03a9)":[20],"+":[21],"\\frac":[22],"12":[23],"\\iint_{\u03a9\\times":[24],"\u03a9}":[25],"\\frac{dx\\,dy}{|x-y|}":[26],"under":[28],"volume":[30,65],"constraint":[31],"$|\u03a9|=V$.":[32],"look":[34],"smooth,":[36],"embedded,":[37],"compact":[38],"surfaces":[39],"$\\partial\u03a9$":[40],"that":[41],"solve":[42],"this":[43],"problem.":[44],"construct":[46],"an":[47],"axially":[48],"symmetric,":[49],"non-minimizing":[50],"solution":[51],"that,":[52],"a":[54,69,75],"sufficiently":[55],"small":[56],"$V>0$,":[57],"resembles":[58],"union":[60],"two":[62],"balls":[63],"with":[64,74],"$V/2$":[66],"connected":[67],"by":[68],"tiny,":[70],"approximately":[71],"catenoidal":[72],"neck":[73],"width":[76],"order":[79],"$V^{\\frac":[80],"43}$.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-03T00:00:00"}
