{"id":"https://openalex.org/W7215922720","doi":"https://doi.org/10.48550/arxiv.2610.01713","title":"Classification of quadratically pinched translators in higher codimension","display_name":"Classification of quadratically pinched translators in higher codimension","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7215922720","doi":"https://doi.org/10.48550/arxiv.2610.01713"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.01713","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01713","pdf_url":"https://arxiv.org/pdf/2610.01713","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/2610.01713","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013982862","display_name":"Debora Impera","orcid":"https://orcid.org/0000-0003-3616-1773","observed_orcids":["https://orcid.org/0000-0003-3616-1773"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Impera, Debora","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086318107","display_name":"Michele Rimoldi","orcid":"https://orcid.org/0000-0003-4353-892X","observed_orcids":["https://orcid.org/0000-0003-4353-892X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rimoldi, Michele","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126704135","display_name":"Francesco Ruatta","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ruatta, Francesco","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":1,"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":1.0,"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":1.0,"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":9.999999747378752e-05,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0,"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/translating-solitons","display_name":"translating solitons","score":0.8840000033378601},{"id":"https://openalex.org/keywords/mean-curvature-flow","display_name":"mean curvature flow","score":0.9990000128746033},{"id":"https://openalex.org/keywords/second-fundamental-form","display_name":"second fundamental form","score":0.9580000042915344},{"id":"https://openalex.org/keywords/omori-yau-maximum-principle","display_name":"Omori-Yau maximum principle","score":0.9539999961853027},{"id":"https://openalex.org/keywords/rigidity-theorems","display_name":"rigidity theorems","score":0.7490000128746033},{"id":"https://openalex.org/keywords/affine-planes","display_name":"affine planes","score":0.5929999947547913},{"id":"https://openalex.org/keywords/higher-codimension","display_name":"higher codimension","score":0.6259999871253967}],"concepts":[{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.8707000017166138},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8396000266075134},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7520999908447266},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.6930999755859375},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4869000017642975},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.47269999980926514},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.46619999408721924},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4528000056743622},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.38909998536109924},{"id":"https://openalex.org/C91709909","wikidata":"https://www.wikidata.org/wiki/Q583960","display_name":"Homothetic transformation","level":2,"score":0.37940001487731934},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.3555000126361847},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35089999437332153},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.2854999899864197},{"id":"https://openalex.org/C154610627","wikidata":"https://www.wikidata.org/wiki/Q382491","display_name":"Affine plane (incidence geometry)","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.2619999945163727},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.2558000087738037}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.01713","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01713","pdf_url":"https://arxiv.org/pdf/2610.01713","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.2610.01713","doi":"https://doi.org/10.48550/arxiv.2610.01713","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.01713","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:2610.01713","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01713","pdf_url":"https://arxiv.org/pdf/2610.01713","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/W7215922720.pdf","grobid_xml":"https://content.openalex.org/works/W7215922720.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7131414912","https://openalex.org/W7215079884"],"related_works":["https://openalex.org/W2883047569","https://openalex.org/W4391602585","https://openalex.org/W2758000727","https://openalex.org/W2339840256","https://openalex.org/W2761812841","https://openalex.org/W3125513853","https://openalex.org/W4410933209","https://openalex.org/W7131414912","https://openalex.org/W1791770697","https://openalex.org/W2027322841"],"abstract_inverted_index":{"We":[0,21],"study":[1],"complete":[2,33],"translating":[3],"solitons":[4],"for":[5,46,85,105,131],"the":[6,17,28,60,76,106,122,142],"mean":[7,87],"curvature":[8,88],"flow":[9],"in":[10,39,64,73,154],"arbitrary":[11],"codimension":[12,24,82],"under":[13,121],"quadratic":[14],"pinching":[15,77,124],"of":[16],"second":[18],"fundamental":[19],"form.":[20],"prove":[22],"a":[23,32,119,139,150],"reduction":[25,83],"theorem":[26],"at":[27],"Andrews-Baker":[29],"threshold:":[30],"if":[31],"$n$-dimensional":[34],"connected":[35],"translator":[36,61,143],"isometrically":[37],"immersed":[38],"$(\\mathbb{R}^{n+p},\\langle\\cdot,\\cdot\\rangle)$":[40],"satisfies":[41],"\\[":[42,126],"|B|^2\\leq":[43,127],"\\left(\\frac{4}{3n}-\\varepsilon_{0}\\right)|H|^2":[44],"\\]":[45,130],"some":[47],"$\\varepsilon_{0}>0$,":[48],"then":[49],"either":[50,145],"it":[51],"is":[52,62,92,144,162],"an":[53,65,114,146,155],"affine":[54,67,147,157],"$n$-plane":[55],"or":[56,149],"$|H|>0$":[57],"everywhere":[58],"and":[59,113],"contained":[63,153],"$(n+1)$-dimensional":[66,156],"subspace.":[68,158],"In":[69],"particular,":[70],"this":[71],"improves":[72],"low":[74],"dimensions":[75],"range":[78],"previously":[79],"obtained":[80],"from":[81],"results":[84],"ancient":[86],"flows.":[89],"Our":[90],"proof":[91],"purely":[93],"elliptic:":[94],"viewing":[95],"translators":[96],"as":[97],"weighted":[98],"minimal":[99],"submanifolds,":[100],"we":[101,137],"combine":[102],"Simons-type":[103],"identities":[104],"drift":[107],"Laplacian":[108],"with":[109,133],"refined":[110],"gradient":[111],"estimates":[112],"Omori-Yau":[115],"maximum":[116],"principle.":[117],"As":[118],"consequence,":[120],"stronger":[123],"condition":[125],"(c_n-\\varepsilon_{0})|H|^2,\\qquad":[128],"c_n=\\min\\left\\{\\frac{4}{3n},\\frac{1}{n-2}\\right\\}":[129],"$n\\geq3$,":[132],"$c_n=2/3$":[134],"when":[135],"$n=2$,":[136],"obtain":[138],"rigidity":[140],"theorem:":[141],"plane":[148],"bowl":[151],"soliton":[152],"No":[159],"entropy":[160],"assumption":[161],"required.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}