{"id":"https://openalex.org/W7162570904","doi":"https://doi.org/10.4230/lipics.socg.2026.37","title":"A Free Lunch: Manifolds of Positive Reach Can Be Smoothed Without Decreasing the Reach","display_name":"A Free Lunch: Manifolds of Positive Reach Can Be Smoothed Without Decreasing the Reach","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7162570904","doi":"https://doi.org/10.4230/lipics.socg.2026.37"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25843","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.37","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.37/LIPIcs.SoCG.2026.37.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.37/LIPIcs.SoCG.2026.37.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137096150","display_name":"Hana Dal Poz Kou\u0159imsk\u00e1","orcid":"https://orcid.org/0000-0001-7841-0091"},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dal Poz Kou\u0159imsk\u00e1, Hana","raw_affiliation_strings":["University of Potsdam, Germany"],"raw_orcid":"https://orcid.org/0000-0001-7841-0091","affiliations":[{"raw_affiliation_string":"University of Potsdam, Germany","institution_ids":["https://openalex.org/I176453806"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137139930","display_name":"Andr\u00e9 Lieutier","orcid":"https://orcid.org/0000-0001-9517-4641"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lieutier, Andr\u00e9","raw_affiliation_strings":["Aix-en-Provence, France"],"raw_orcid":"https://orcid.org/0000-0001-9517-4641","affiliations":[{"raw_affiliation_string":"Aix-en-Provence, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5137181193","display_name":"Mathijs Wintraecken","orcid":"https://orcid.org/0000-0002-7472-2220"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Wintraecken, Mathijs","raw_affiliation_strings":["Inria Centre d'Universit\u00e9 C\u00f4te d'Azur, Sophia Antipolis, France"],"raw_orcid":"https://orcid.org/0000-0002-7472-2220","affiliations":[{"raw_affiliation_string":"Inria Centre d'Universit\u00e9 C\u00f4te d'Azur, Sophia Antipolis, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.63471628,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.6531000137329102,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.6531000137329102,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.1273999959230423,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.03200000151991844,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/manifold","display_name":"Manifold (fluid mechanics)","score":0.7501000165939331},{"id":"https://openalex.org/keywords/closed-manifold","display_name":"Closed manifold","score":0.6003000140190125},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.5990999937057495},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.5608999729156494},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5561000108718872},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.4794999957084656},{"id":"https://openalex.org/keywords/pseudo-riemannian-manifold","display_name":"Pseudo-Riemannian manifold","score":0.4462999999523163},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.44130000472068787},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.41670000553131104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7565000057220459},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.7501000165939331},{"id":"https://openalex.org/C74349738","wikidata":"https://www.wikidata.org/wiki/Q1517914","display_name":"Closed manifold","level":3,"score":0.6003000140190125},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.5990999937057495},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.5608999729156494},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5561000108718872},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.4794999957084656},{"id":"https://openalex.org/C121705324","wikidata":"https://www.wikidata.org/wiki/Q1510587","display_name":"Pseudo-Riemannian manifold","level":4,"score":0.4462999999523163},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.44130000472068787},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.41670000553131104},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.39899998903274536},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.39899998903274536},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39250001311302185},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.37220001220703125},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.3603000044822693},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33250001072883606},{"id":"https://openalex.org/C153120616","wikidata":"https://www.wikidata.org/wiki/Q17068315","display_name":"Manifold alignment","level":4,"score":0.32919999957084656},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.32710000872612},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.31700000166893005},{"id":"https://openalex.org/C32518243","wikidata":"https://www.wikidata.org/wiki/Q907926","display_name":"Holonomy","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C516171914","wikidata":"https://www.wikidata.org/wiki/Q1224402","display_name":"Differential topology","level":5,"score":0.2833000123500824},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.2572000026702881},{"id":"https://openalex.org/C149944404","wikidata":"https://www.wikidata.org/wiki/Q2392464","display_name":"Tangent cone","level":3,"score":0.2524999976158142}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:25843","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.37","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.37/LIPIcs.SoCG.2026.37.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},{"id":"doi:10.4230/lipics.socg.2026.37","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.37","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25843","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.37","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.37/LIPIcs.SoCG.2026.37.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4274670481681824,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7162570904.pdf","grobid_xml":"https://content.openalex.org/works/W7162570904.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Assumptions":[0],"on":[1],"the":[2,8,38,41,72,92,96,147],"reach":[3,59,80,106,141],"are":[4,34,102,153],"crucial":[5],"for":[6,26,134,156],"ensuring":[7],"correctness":[9],"of":[10,119],"many":[11],"geometric":[12],"and":[13,20,24,98,104,121],"topological":[14],"algorithms,":[15],"including":[16],"triangulation,":[17],"manifold":[18,42,56,68,78,85,97],"reconstruction":[19],"learning,":[21],"homotopy":[22],"reconstruction,":[23],"methods":[25],"estimating":[27],"curvature":[28],"or":[29,136],"reach.":[30,73],"However,":[31],"these":[32],"assumptions":[33],"often":[35],"coupled":[36],"with":[37,57,79,138,146],"requirement":[39],"that":[40,54,86,129],"be":[43,61],"smooth,":[44],"typically":[45],"at":[46,107],"least":[47,108],"C\u00b2.":[48],"In":[49],"this":[50],"paper,":[51],"we":[52,82],"prove":[53],"any":[55],"positive":[58],"can":[60],"approximated":[62],"arbitrarily":[63],"well":[64],"by":[65],"a":[66,77,84,139],"C^\u221e":[67],"without":[69],"significantly":[70],"reducing":[71],"More":[74],"precisely,":[75],"given":[76],"R,":[81],"construct":[83],"is":[87],"\u03b5-close":[88],"to":[89,144],"it":[90],"in":[91],"C\u00b9":[93],"sense":[94],"(both":[95],"its":[99],"tangent":[100],"spaces":[101],"close),":[103],"has":[105],"R-\u03b5.":[109],"The":[110],"proof":[111],"employs":[112],"techniques":[113],"from":[114],"differential":[115],"topology":[116],"-":[117],"partitions":[118],"unity":[120],"smoothing":[122],"using":[123],"convolution":[124],"kernels.":[125],"This":[126],"result":[127],"implies":[128],"nearly":[130],"all":[131],"theorems":[132],"established":[133],"C\u00b2":[135],"manifolds":[137,145],"certain":[140],"naturally":[142],"extend":[143],"same":[148],"reach,":[149],"even":[150],"if":[151],"they":[152],"not":[154],"C\u00b2,":[155],"free!":[157]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-28T00:00:00"}
