{"id":"https://openalex.org/W7213286370","doi":"https://doi.org/10.48550/arxiv.2609.14194","title":"A counterexample to quasiconcavity for the Gaussian $p$-Capacity potentials in convex rings","display_name":"A counterexample to quasiconcavity for the Gaussian $p$-Capacity potentials in convex rings","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213286370","doi":"https://doi.org/10.48550/arxiv.2609.14194"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14194","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14194","pdf_url":"https://arxiv.org/pdf/2609.14194","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/2609.14194","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122917741","display_name":"Lei Qin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qin, Lei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5122917741"],"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":0.7020999789237976,"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":0.7020999789237976,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.19419999420642853,"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":0.06270000338554382,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quasi-concavity","display_name":"quasi-concavity","score":0.9169999957084656},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.7200000286102295},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.6039999723434448},{"id":"https://openalex.org/keywords/strictly-convex-domains","display_name":"strictly convex domains","score":0.5870000123977661}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.848800003528595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6589000225067139},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5853000283241272},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5393000245094299},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5182999968528748},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45179998874664307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4399000108242035},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.41359999775886536},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4065000116825104},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3465000092983246},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.33219999074935913},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3000999987125397},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.2824999988079071},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.25940001010894775}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14194","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14194","pdf_url":"https://arxiv.org/pdf/2609.14194","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.2609.14194","doi":"https://doi.org/10.48550/arxiv.2609.14194","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14194","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:2609.14194","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14194","pdf_url":"https://arxiv.org/pdf/2609.14194","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/W7213286370.pdf","grobid_xml":"https://content.openalex.org/works/W7213286370.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1866311589","https://openalex.org/W7123504341","https://openalex.org/W7139918456","https://openalex.org/W7147354294","https://openalex.org/W7204957236"],"related_works":["https://openalex.org/W233650615","https://openalex.org/W4296397835","https://openalex.org/W2227322464","https://openalex.org/W1991546909","https://openalex.org/W2333309610","https://openalex.org/W2046754273","https://openalex.org/W2318319359","https://openalex.org/W2026472509","https://openalex.org/W6929087158","https://openalex.org/W7098948052"],"abstract_inverted_index":{"We":[0],"construct":[1],"a":[2,9,24],"smooth,":[3],"strictly":[4],"convex":[5],"ring":[6],"that":[7],"admit":[8],"unique":[10],"solution":[11],"of":[12],"Gaussian":[13],"$p$-Capacity":[14],"problem":[15],"whose":[16],"super-level":[17],"sets":[18],"are":[19],"nonconvex.":[20],"This":[21],"result":[22],"provide":[23],"negative":[25],"answer.":[26]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}