{"id":"https://openalex.org/W7223889753","doi":"https://doi.org/10.48550/arxiv.2610.33825","title":"Critical metrics for the Dirac-Yamabe eigenvalue ratio and Einstein-Dirac equations","display_name":"Critical metrics for the Dirac-Yamabe eigenvalue ratio and Einstein-Dirac equations","publication_year":2026,"publication_date":"2026-10-24","ids":{"openalex":"https://openalex.org/W7223889753","doi":"https://doi.org/10.48550/arxiv.2610.33825"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.33825","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33825","pdf_url":"https://arxiv.org/pdf/2610.33825","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.33825","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115911619","display_name":"Mehdi Eddaoudi","orcid":"https://orcid.org/0009-0005-8687-292X","observed_orcids":["https://orcid.org/0009-0005-8687-292X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Eddaoudi, Mehdi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5115911619"],"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":0.8500999808311462,"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":0.8500999808311462,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.059700001031160355,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.03970000147819519,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/critical-metrics","display_name":"critical metrics","score":0.8510000109672546},{"id":"https://openalex.org/keywords/dirac-operator","display_name":"Dirac operator","score":0.8029999732971191},{"id":"https://openalex.org/keywords/conformal-laplacian","display_name":"conformal Laplacian","score":0.9549999833106995},{"id":"https://openalex.org/keywords/eigenvalue-ratio","display_name":"eigenvalue ratio","score":0.8579999804496765},{"id":"https://openalex.org/keywords/einstein-dirac-equations","display_name":"Einstein-Dirac equations","score":0.8610000014305115},{"id":"https://openalex.org/keywords/energy-momentum-tensor","display_name":"energy-momentum tensor","score":0.7739999890327454},{"id":"https://openalex.org/keywords/harmonic-sections","display_name":"harmonic sections","score":0.7889999747276306},{"id":"https://openalex.org/keywords/yamabe-constant","display_name":"Yamabe constant","score":0.8870000243186951},{"id":"https://openalex.org/keywords/spin-manifolds","display_name":"spin manifolds","score":0.8949999809265137},{"id":"https://openalex.org/keywords/conformal-geometry","display_name":"conformal geometry","score":0.7850000262260437},{"id":"https://openalex.org/keywords/round-spheres","display_name":"round spheres","score":0.8349999785423279}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7383999824523926},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.6919999718666077},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5604000091552734},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5579000115394592},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5192000269889832},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5142999887466431},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.501800000667572},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.492900013923645},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4875999987125397},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4553000032901764},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44449999928474426},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4359000027179718},{"id":"https://openalex.org/C203269682","wikidata":"https://www.wikidata.org/wiki/Q7116898","display_name":"p-Laplacian","level":3,"score":0.34209999442100525},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3172999918460846},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.295199990272522},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.28940001130104065},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C158650840","wikidata":"https://www.wikidata.org/wiki/Q907439","display_name":"Dirac operator","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2554999887943268}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.33825","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33825","pdf_url":"https://arxiv.org/pdf/2610.33825","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.2610.33825","doi":"https://doi.org/10.48550/arxiv.2610.33825","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.33825","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:2610.33825","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33825","pdf_url":"https://arxiv.org/pdf/2610.33825","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/G1947404341","display_name":"Geometric and analytic properties of metric measure spaces with spectral curvature constraints, with applications to manifold learning","funder_award_id":"G0DBZ23N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223889753.pdf","grobid_xml":"https://content.openalex.org/works/W7223889753.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7154704743","https://openalex.org/W2885648155","https://openalex.org/W2145304928","https://openalex.org/W1794488974","https://openalex.org/W7135054788","https://openalex.org/W7223202020","https://openalex.org/W2729720141","https://openalex.org/W1632697708","https://openalex.org/W7154044744","https://openalex.org/W4200634032"],"abstract_inverted_index":{"Let":[0],"$(M^n,g)$":[1],"be":[2],"a":[3,42],"closed":[4],"spin":[5],"manifold":[6],"of":[7,55,78],"dimension":[8],"$n\\geq":[9],"3$":[10],"with":[11],"positive":[12],"Yamabe":[13],"constant.":[14],"We":[15,52],"prove":[16,67],"that":[17,68],"critical":[18],"metrics":[19],"for":[20,58],"the":[21,30,36,75,79],"mixed":[22],"eigenvalue":[23],"ratio":[24],"$\\mathcal":[25,69],"H(g)=\\frac{\u03bb_1(D_g)^2}{\u03bb_1(L_g)},$":[26],"where":[27],"$D_g$":[28],"is":[29,35,71],"Dirac":[31],"operator":[32],"and":[33,61],"$L_g$":[34],"conformal":[37,76],"Laplacian":[38],"are":[39],"characterized":[40],"by":[41],"harmonic":[43],"section":[44],"whose":[45],"energy-momentum":[46],"tensor":[47],"satisfies":[48],"an":[49,64],"Einstein--Dirac":[50],"equation.":[51],"discuss":[53],"consequences":[54],"this":[56],"result":[57],"Hijazi's":[59],"inequality,":[60],"we":[62],"construct":[63],"example":[65],"to":[66],"H$":[70],"unbounded":[72],"above":[73],"within":[74],"class":[77],"round":[80],"sphere.":[81]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-10-28T00:00:00"}
