{"id":"https://openalex.org/W7213340204","doi":"https://doi.org/10.48550/arxiv.2609.15858","title":"Global Curvature Estimates for k-Convex Hypersurfaces","display_name":"Global Curvature Estimates for k-Convex Hypersurfaces","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213340204","doi":"https://doi.org/10.48550/arxiv.2609.15858"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15858","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15858","pdf_url":"https://arxiv.org/pdf/2609.15858","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/2609.15858","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112558544","display_name":"Fengrui Yang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yang, Fengrui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5112558544"],"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":0.9692000150680542,"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":0.9692000150680542,"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":0.01850000023841858,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.006899999920278788,"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/mobius-transformations","display_name":"M\u00f6bius transformations","score":0.7559999823570251},{"id":"https://openalex.org/keywords/hyperbolic-polynomials","display_name":"hyperbolic polynomials","score":0.9430000185966492},{"id":"https://openalex.org/keywords/log-concavity","display_name":"log-concavity","score":0.9700000286102295},{"id":"https://openalex.org/keywords/coercive-estimates","display_name":"coercive estimates","score":0.7860000133514404},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"maximum principle","score":0.8379999995231628},{"id":"https://openalex.org/keywords/star-shaped-hypersurfaces","display_name":"star-shaped hypersurfaces","score":0.875},{"id":"https://openalex.org/keywords/fully-nonlinear-equations","display_name":"fully nonlinear equations","score":0.652999997138977},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"mean curvature","score":0.5649999976158142}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7894999980926514},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.7477999925613403},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5461000204086304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5335999727249146},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5051000118255615},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.47609999775886536},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.47049999237060547},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4255000054836273},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4156000018119812},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.41290000081062317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3950999975204468},{"id":"https://openalex.org/C2778433361","wikidata":"https://www.wikidata.org/wiki/Q7268358","display_name":"Quadratic differential","level":3,"score":0.32899999618530273},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C2983854663","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Negative curvature","level":3,"score":0.29159998893737793},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29089999198913574},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2572000026702881}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.15858","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15858","pdf_url":"https://arxiv.org/pdf/2609.15858","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.2609.15858","doi":"https://doi.org/10.48550/arxiv.2609.15858","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15858","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:2609.15858","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15858","pdf_url":"https://arxiv.org/pdf/2609.15858","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/W7213340204.pdf","grobid_xml":"https://content.openalex.org/works/W7213340204.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W2054180334","https://openalex.org/W2544579868","https://openalex.org/W2964159702","https://openalex.org/W2964221336","https://openalex.org/W2964244357","https://openalex.org/W2973188513","https://openalex.org/W3080111066","https://openalex.org/W3111284075","https://openalex.org/W4387085204","https://openalex.org/W4388204721","https://openalex.org/W4392328975","https://openalex.org/W4413423238","https://openalex.org/W4416917285","https://openalex.org/W7204480557"],"related_works":["https://openalex.org/W3042449587","https://openalex.org/W3007678709","https://openalex.org/W7169881717","https://openalex.org/W4404165712","https://openalex.org/W2964159702","https://openalex.org/W3014147771","https://openalex.org/W3111284075","https://openalex.org/W7169554197","https://openalex.org/W4388204721","https://openalex.org/W4392820177"],"abstract_inverted_index":{"Establishing":[0],"global":[1,69],"curvature":[2,9,70],"estimates":[3],"for":[4,47,72],"$k$-convex":[5,76],"solutions":[6],"of":[7,37],"prescribed":[8],"equations":[10,20],"is":[11,43],"a":[12,26,44,62],"longstanding":[13],"problem":[14],"in":[15,56,78],"fully":[16],"nonlinear":[17],"partial":[18],"differential":[19],"and":[21],"geometric":[22],"analysis.":[23],"We":[24],"develop":[25],"new":[27],"approach":[28],"that":[29],"combines":[30],"fractional-linear":[31],"transformations":[32],"with":[33,61],"the":[34,48,53,57,83],"logarithmic":[35],"concavity":[36,64],"hyperbolic":[38],"polynomials.":[39],"The":[40],"key":[41],"step":[42],"coercive":[45],"estimate":[46,67],"quadratic":[49],"forms":[50],"arising":[51],"from":[52],"third-order":[54],"terms":[55],"maximum-principle":[58],"argument.":[59],"Together":[60],"complementary":[63],"inequality,":[65],"this":[66],"yields":[68],"bounds":[71],"closed,":[73],"strictly":[74],"star-shaped":[75],"hypersurfaces":[77],"$\\mathbb{R}^{n+1}$":[79],"satisfying":[80],"$\u03c3_k(\u03ba)=f(X,\u03bd)>0$,":[81],"throughout":[82],"range":[84],"$3\\leq":[85],"k":[86]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}