{"id":"https://openalex.org/W7223087196","doi":"https://doi.org/10.48550/arxiv.2610.28520","title":"The $\u03bb>0$ case for $\u0394u=\u03bb-c e^u$ type equation on high dimensional spheres","display_name":"The $\u03bb>0$ case for $\u0394u=\u03bb-c e^u$ type equation on high dimensional spheres","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223087196","doi":"https://doi.org/10.48550/arxiv.2610.28520"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28520","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28520","pdf_url":"https://arxiv.org/pdf/2610.28520","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/2610.28520","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159186851","display_name":"Yuxuan Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yuxuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159213223","display_name":"Qiang Niu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Niu, Qiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074630580","display_name":"Wubin Zhou","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Wubin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.951200008392334,"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":0.951200008392334,"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":0.04100000113248825,"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/T12351","display_name":"Geometry and complex manifolds","score":0.003100000089034438,"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/high-dimensional-spheres","display_name":"high-dimensional spheres","score":0.7760000228881836},{"id":"https://openalex.org/keywords/axisymmetric-solutions","display_name":"axisymmetric solutions","score":0.7179999947547913},{"id":"https://openalex.org/keywords/liouville-type-equations","display_name":"Liouville-type equations","score":0.6119999885559082},{"id":"https://openalex.org/keywords/prescribed-mean-curvature-equation","display_name":"prescribed mean curvature","score":0.4410000145435333},{"id":"https://openalex.org/keywords/complex-geometries","display_name":"complex geometries","score":0.5099999904632568}],"concepts":[{"id":"https://openalex.org/C35377427","wikidata":"https://www.wikidata.org/wiki/Q3886264","display_name":"Axial symmetry","level":2,"score":0.6151999831199646},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6136999726295471},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5774999856948853},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.5339999794960022},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5044000148773193},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.49869999289512634},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.40619999170303345},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3668000102043152},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.3605000078678131},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2874000072479248},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.27649998664855957},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.25839999318122864}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28520","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28520","pdf_url":"https://arxiv.org/pdf/2610.28520","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.2610.28520","doi":"https://doi.org/10.48550/arxiv.2610.28520","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28520","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:2610.28520","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28520","pdf_url":"https://arxiv.org/pdf/2610.28520","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/W7223087196.pdf","grobid_xml":"https://content.openalex.org/works/W7223087196.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7215083655"],"related_works":["https://openalex.org/W2064618530","https://openalex.org/W2285721507","https://openalex.org/W121728809","https://openalex.org/W2222566091","https://openalex.org/W2950012720","https://openalex.org/W2019317587","https://openalex.org/W4361011763","https://openalex.org/W1982104198","https://openalex.org/W6996488985","https://openalex.org/W2098404304"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"prescribed":[2],"Chern":[3],"scalar":[4],"curvature":[5],"problems":[6],"in":[7],"complex":[8],"geometry,":[9],"we":[10,26],"study":[11],"the":[12,28,42],"equation":[13],"$\u0394_{\\mathbb":[14],"S^{N-1}}V+\u03bb(e^V-1)=0$":[15],"with":[16,24],"$\u03bb>0$":[17],"on":[18],"spheres.":[19],"For":[20],"$N\\ge4$":[21],"and":[22,39],"$\u03bb>2(N-2)$":[23],"$\u03bb\\ne2N$,":[25],"prove":[27],"existence":[29],"of":[30],"a":[31],"nonconstant":[32],"smooth":[33],"solution":[34],"that":[35],"is":[36],"axially":[37],"symmetric":[38,40],"about":[41],"equator.":[43]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-22T00:00:00"}