{"id":"https://openalex.org/W7213587401","doi":"https://doi.org/10.48550/arxiv.2609.19168","title":"Bounded curvature manifolds without Euclidean isometric immersions of bounded mean curvature","display_name":"Bounded curvature manifolds without Euclidean isometric immersions of bounded mean curvature","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213587401","doi":"https://doi.org/10.48550/arxiv.2609.19168"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.19168","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19168","pdf_url":"https://arxiv.org/pdf/2609.19168","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/2609.19168","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136697219","display_name":"Haoxuan Cheng","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cheng, Haoxuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5136697219"],"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":0.8320000171661377,"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":0.8320000171661377,"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":0.16500000655651093,"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/T12351","display_name":"Geometry and complex manifolds","score":0.000699999975040555,"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/bounded-mean-curvature","display_name":"bounded mean curvature","score":0.7940000295639038},{"id":"https://openalex.org/keywords/isometric-immersions","display_name":"isometric immersions","score":0.7829999923706055},{"id":"https://openalex.org/keywords/complete-riemannian-metrics","display_name":"complete Riemannian metrics","score":0.7250000238418579},{"id":"https://openalex.org/keywords/injectivity-radius","display_name":"injectivity radius","score":0.7400000095367432},{"id":"https://openalex.org/keywords/second-fundamental-form","display_name":"second fundamental form","score":0.7250000238418579},{"id":"https://openalex.org/keywords/counterexample-construction","display_name":"counterexample construction","score":0.42899999022483826},{"id":"https://openalex.org/keywords/conformal-blocks","display_name":"conformal blocks","score":0.6959999799728394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7928000092506409},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7627000212669373},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5101000070571899},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5054000020027161},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.47510001063346863},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4706000089645386},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.460999995470047},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.43810001015663147},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.43709999322891235},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4016999900341034},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.3871999979019165},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.3865000009536743},{"id":"https://openalex.org/C199068039","wikidata":"https://www.wikidata.org/wiki/Q574523","display_name":"Immersion (mathematics)","level":2,"score":0.37220001220703125},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.3619999885559082},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.36160001158714294},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.35100001096725464},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.31540000438690186},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.30059999227523804},{"id":"https://openalex.org/C119830904","wikidata":"https://www.wikidata.org/wiki/Q233220","display_name":"Second fundamental form","level":4,"score":0.29820001125335693},{"id":"https://openalex.org/C183517385","wikidata":"https://www.wikidata.org/wiki/Q855112","display_name":"Riemann curvature tensor","level":3,"score":0.29319998621940613},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.29179999232292175},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C14196021","wikidata":"https://www.wikidata.org/wiki/Q7240881","display_name":"Prescribed scalar curvature problem","level":5,"score":0.25369998812675476},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.19168","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19168","pdf_url":"https://arxiv.org/pdf/2609.19168","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.2609.19168","doi":"https://doi.org/10.48550/arxiv.2609.19168","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.19168","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:2609.19168","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19168","pdf_url":"https://arxiv.org/pdf/2609.19168","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213587401.pdf","grobid_xml":"https://content.openalex.org/works/W7213587401.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4406757839","https://openalex.org/W4415109326"],"related_works":["https://openalex.org/W7215725445","https://openalex.org/W2148616724","https://openalex.org/W1974738844","https://openalex.org/W2118815436","https://openalex.org/W2170374728","https://openalex.org/W2116759045","https://openalex.org/W1991361273","https://openalex.org/W2080763204","https://openalex.org/W2005919526","https://openalex.org/W2989383227"],"abstract_inverted_index":{"For":[0],"every":[1],"integer":[2],"$n\\ge2$,":[3],"we":[4],"construct":[5,64],"a":[6,34],"smooth":[7],"complete":[8],"Riemannian":[9],"metric":[10],"$G_n$":[11],"on":[12],"$\\mathbb{R}^n$":[13],"with":[14],"full":[15,102],"curvature":[16,71],"norm":[17],"at":[18,24],"most":[19],"one":[20,26],"and":[21],"injectivity":[22],"radius":[23],"least":[25],"for":[27,68],"which":[28,69],"no":[29],"$C^2$":[30],"isometric":[31],"immersion":[32],"into":[33],"finite-dimensional":[35],"Euclidean":[36,84],"space":[37],"has":[38],"bounded":[39,45,73,101],"mean":[40],"curvature.":[41,103],"In":[42],"dimension":[43],"two,":[44],"second":[46],"fundamental":[47],"form":[48],"would":[49],"give":[50],"uniformly":[51],"controlled":[52],"finite":[53,76],"Jacobian":[54,77],"representations":[55],"of":[56,59,100],"the":[57,60,70,75,97],"Laplacian":[58],"conformal":[61,66],"factor.":[62],"We":[63],"disjoint":[65],"blocks":[67],"remains":[72],"while":[74],"representation":[78],"cost":[79],"tends":[80],"to":[81],"infinity.":[82],"Taking":[83],"products":[85],"gives":[86],"all":[87],"higher":[88],"dimensions.":[89],"The":[90],"result":[91],"answers":[92],"Yau's":[93],"Problem~52":[94],"negatively":[95],"under":[96],"stronger":[98],"assumption":[99]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-19T00:00:00"}