{"id":"https://openalex.org/W7214014641","doi":"https://doi.org/10.48550/arxiv.2609.24549","title":"Interior estimates for Hessian quotient equations","display_name":"Interior estimates for Hessian quotient equations","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214014641","doi":"https://doi.org/10.48550/arxiv.2609.24549"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.24549","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24549","pdf_url":"https://arxiv.org/pdf/2609.24549","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/2609.24549","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082371563","display_name":"Guohuan Qiu","orcid":"https://orcid.org/0000-0002-2654-4044","observed_orcids":["https://orcid.org/0000-0002-2654-4044"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiu, Guohuan","raw_affiliation_strings":["Institute of Mathematics , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , 55 Zhongguancun East Road , Beijing 100190 , China","State Key Laboratory of Mathematical Sciences , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , Beijing 100190 , China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , 55 Zhongguancun East Road , Beijing 100190 , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"raw_affiliation_string":"State Key Laboratory of Mathematical Sciences , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , Beijing 100190 , China;","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042119988","display_name":"Jin Yan","orcid":"https://orcid.org/0000-0002-0308-6407","observed_orcids":["https://orcid.org/0000-0002-0308-6407","https://orcid.org/0009-0007-9494-0528"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan, Jin","raw_affiliation_strings":["Institute of Mathematics , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , 55 Zhongguancun East Road , Beijing 100190 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , 55 Zhongguancun East Road , Beijing 100190 , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"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":4,"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":0.8438000082969666,"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":0.8438000082969666,"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":0.13770000636577606,"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":0.0027000000700354576,"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/interior-estimates","display_name":"interior estimates","score":0.6930000185966492},{"id":"https://openalex.org/keywords/admissible-solutions","display_name":"admissible solutions","score":0.8059999942779541},{"id":"https://openalex.org/keywords/degree-difference","display_name":"degree difference","score":0.5070000290870667}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8862000107765198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8375999927520752},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7803999781608582},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6743000149726868},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.6308000087738037},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5554999709129333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49889999628067017},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4952000081539154},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48069998621940613},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.44760000705718994},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4449000060558319},{"id":"https://openalex.org/C40753290","wikidata":"https://www.wikidata.org/wiki/Q1139111","display_name":"Quotient space (topology)","level":3,"score":0.33489999175071716},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2867000102996826},{"id":"https://openalex.org/C2778158742","wikidata":"https://www.wikidata.org/wiki/Q1665115","display_name":"Rayleigh quotient","level":3,"score":0.2775999903678894}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.24549","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24549","pdf_url":"https://arxiv.org/pdf/2609.24549","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.2609.24549","doi":"https://doi.org/10.48550/arxiv.2609.24549","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.24549","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:2609.24549","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24549","pdf_url":"https://arxiv.org/pdf/2609.24549","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":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214014641.pdf","grobid_xml":"https://content.openalex.org/works/W7214014641.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W2011186763","https://openalex.org/W2027090993","https://openalex.org/W2029849417","https://openalex.org/W2045451260","https://openalex.org/W2061885154","https://openalex.org/W2066959726","https://openalex.org/W2085360607","https://openalex.org/W2166166211","https://openalex.org/W2171416746","https://openalex.org/W2544579868","https://openalex.org/W2766975214","https://openalex.org/W2999420497","https://openalex.org/W3170952378","https://openalex.org/W4234850258","https://openalex.org/W4388650776","https://openalex.org/W4393674235","https://openalex.org/W4398792135","https://openalex.org/W4406072733","https://openalex.org/W4408419084","https://openalex.org/W4411805975","https://openalex.org/W4415024491","https://openalex.org/W4415962922","https://openalex.org/W4416192305","https://openalex.org/W4416713165","https://openalex.org/W7115599861","https://openalex.org/W7135167429","https://openalex.org/W7137827840","https://openalex.org/W7156596854","https://openalex.org/W7171468062","https://openalex.org/W7203716784","https://openalex.org/W7203774676","https://openalex.org/W7203876830","https://openalex.org/W7204175919","https://openalex.org/W7207571619"],"related_works":["https://openalex.org/W7203876830","https://openalex.org/W4382025605","https://openalex.org/W2066959726","https://openalex.org/W7204175919","https://openalex.org/W4417325992","https://openalex.org/W4411805975","https://openalex.org/W7221775687","https://openalex.org/W7156596854","https://openalex.org/W3130825970","https://openalex.org/W7166168263"],"abstract_inverted_index":{"We":[0],"prove":[1],"interior":[2],"Hessian":[3,12],"estimates":[4],"in":[5,25],"arbitrary":[6],"dimensions":[7],"for":[8],"admissible":[9],"solutions":[10],"of":[11],"quotient":[13],"equations":[14],"with":[15],"constant":[16],"right-hand":[17],"side,":[18],"when":[19],"the":[20],"numerator":[21],"and":[22,51],"denominator":[23],"differ":[24],"degree":[26,35],"by":[27],"one":[28],"or":[29],"two.":[30],"Counterexamples":[31],"show":[32],"that":[33],"this":[34],"range":[36],"is":[37],"optimal.":[38],"The":[39],"proof":[40],"combines":[41],"a":[42,47,52],"new":[43],"nonlinear":[44],"comparison":[45],"function,":[46],"doubling":[48],"maximum":[49],"principle,":[50],"Pogorelov":[53],"estimate.":[54]},"counts_by_year":[{"year":2026,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}