{"id":"https://openalex.org/W7221015209","doi":"https://doi.org/10.48550/arxiv.2610.07852","title":"The interpolation method for the complex Hessian equation on compact K\u00e4hler manifolds","display_name":"The interpolation method for the complex Hessian equation on compact K\u00e4hler manifolds","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7221015209","doi":"https://doi.org/10.48550/arxiv.2610.07852"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07852","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07852","pdf_url":"https://arxiv.org/pdf/2610.07852","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/2610.07852","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061106902","display_name":"Jiaogen Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Jiaogen","raw_affiliation_strings":["School of Mathematics , Hefei University of Technology , Hefei 230009 , P.R. China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Hefei University of Technology , Hefei 230009 , P.R. China;","institution_ids":["https://openalex.org/I16365422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157939502","display_name":"Xi Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]},{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Xi","raw_affiliation_strings":["School of Mathematics , Hefei University of Technology , Hefei 230009 , P.R. China;","School of Mathematics and Statistics , Nanjing University of Science and Technology , Nanjing 210094 , China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Hefei University of Technology , Hefei 230009 , P.R. China;","institution_ids":["https://openalex.org/I16365422"]},{"raw_affiliation_string":"School of Mathematics and Statistics , Nanjing University of Science and Technology , Nanjing 210094 , China;","institution_ids":["https://openalex.org/I36399199"]}]}],"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":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/T12351","display_name":"Geometry and complex manifolds","score":0.9761000275611877,"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"}},"topics":[{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.9761000275611877,"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"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.012400000356137753,"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":0.008500000461935997,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/complex-hessian-equations","display_name":"complex Hessian equations","score":0.9240000247955322},{"id":"https://openalex.org/keywords/compact-kahler-manifolds","display_name":"compact K\u00e4hler manifolds","score":0.9929999709129333},{"id":"https://openalex.org/keywords/interpolation-methods","display_name":"interpolation methods","score":0.6480000019073486},{"id":"https://openalex.org/keywords/bisectional-curvature","display_name":"bisectional curvature","score":0.8539999723434448},{"id":"https://openalex.org/keywords/gradient-estimates","display_name":"gradient estimates","score":0.6819999814033508},{"id":"https://openalex.org/keywords/oscillation-of-solutions","display_name":"oscillation of solutions","score":0.7509999871253967},{"id":"https://openalex.org/keywords/blow-up-technique","display_name":"blow-up technique","score":0.7279999852180481}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8087000250816345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.689300000667572},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6292999982833862},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6100999712944031},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5997999906539917},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5986999869346619},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.5787000060081482},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46869999170303345},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.3319999873638153},{"id":"https://openalex.org/C15980293","wikidata":"https://www.wikidata.org/wiki/Q5164368","display_name":"Constraint algorithm","level":3,"score":0.3246999979019165},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.3160000145435333},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07852","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07852","pdf_url":"https://arxiv.org/pdf/2610.07852","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.2610.07852","doi":"https://doi.org/10.48550/arxiv.2610.07852","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07852","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.07852","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07852","pdf_url":"https://arxiv.org/pdf/2610.07852","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/G1231468753","display_name":null,"funder_award_id":"12141104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G222581545","display_name":null,"funder_award_id":"11721101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5123990054","display_name":null,"funder_award_id":"11801535","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7197553430","display_name":null,"funder_award_id":"2020YFA0713100","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320328099","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221015209.pdf","grobid_xml":"https://content.openalex.org/works/W7221015209.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7214716720","https://openalex.org/W7215096156","https://openalex.org/W2252702938","https://openalex.org/W7092305991","https://openalex.org/W3022472896","https://openalex.org/W2087516310","https://openalex.org/W4415381659","https://openalex.org/W7220746322","https://openalex.org/W3167112923","https://openalex.org/W2803320745"],"abstract_inverted_index":{"In":[0],"current":[1],"work,":[2],"we":[3,31,46,72],"delve":[4],"into":[5],"the":[6,22,26,29,34,54,62,66,76,80,87,90],"study":[7],"of":[8,28,79],"complex":[9,81],"Hessian":[10,82],"equations":[11,83],"on":[12,20],"compact":[13],"K\u00e4hler":[14],"manifolds.":[15],"By":[16],"imposing":[17],"a":[18,57],"constraint":[19],"both":[21],"bisectional":[23],"curvature":[24],"and":[25],"oscillation":[27],"solution,":[30],"demonstrate":[32,73],"that":[33,74],"Laplacian":[35],"estimate":[36,52,93],"can":[37],"be":[38],"linearly":[39],"controlled":[40],"by":[41],"its":[42],"gradient":[43,51,92],"estimate.":[44],"Consequently,":[45],"are":[47],"able":[48],"to":[49,64],"derive":[50],"for":[53],"solution":[55],"using":[56],"standard":[58],"interpolation":[59],"argument,":[60],"without":[61],"need":[63],"employ":[65],"blow-up":[67],"technique.":[68],"As":[69],"an":[70],"application,":[71],"when":[75],"right-hand":[77],"side":[78],"approximate":[84],"1":[85],"in":[86],"$L^1$":[88],"norm,":[89],"desired":[91],"is":[94],"obtained.":[95]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}
