{"id":"https://openalex.org/W7160290261","doi":"https://doi.org/10.48550/arxiv.2605.02770","title":"Implicit Minimal Surfaces for Bijective Correspondences","display_name":"Implicit Minimal Surfaces for Bijective Correspondences","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W7160290261","doi":"https://doi.org/10.48550/arxiv.2605.02770"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.02770","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02770","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.02770","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041633721","display_name":"\u00c9tienne Corman","orcid":"https://orcid.org/0009-0002-9401-2362"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Corman, Etienne","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135398701","display_name":"Yousuf Soliman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Soliman, Yousuf","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046723089","display_name":"Robin Magnet","orcid":"https://orcid.org/0000-0002-2192-411X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Magnet, Robin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135390940","display_name":"Mark Gillespie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gillespie, Mark","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":false,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.11379999667406082,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.11379999667406082,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.0908999964594841,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.062199998646974564,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8888999819755554},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.6014999747276306},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.49239999055862427},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.48559999465942383},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4805999994277954},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.4242999851703644},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.40560001134872437},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.400299996137619},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.3910999894142151}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8888999819755554},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.6014999747276306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5806999802589417},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.49239999055862427},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.48559999465942383},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4805999994277954},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4659999907016754},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.4242999851703644},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.40560001134872437},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3910999894142151},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.34850001335144043},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3264000117778778},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.3086000084877014},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2833999991416931},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.28029999136924744},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2775999903678894},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C138673069","wikidata":"https://www.wikidata.org/wiki/Q322229","display_name":"Tracing","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.25769999623298645},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2526000142097473}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.02770","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02770","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.02770","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02770","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,202],"introduce":[1],"an":[2],"implicit":[3,220],"representation":[4,221],"of":[5,20,55,113,144,160,177,187,198,207],"continuous,":[6],"bijective,":[7],"orientation-preserving":[8],"maps":[9,22],"between":[10,131],"genus":[11],"zero":[12,158],"surfaces":[13,132],"with":[14,234],"or":[15],"without":[16],"boundary.":[17],"The":[18,61,124],"distortion":[19,176],"these":[21],"can":[23,96,152,180],"easily":[24],"be":[25,153,181],"minimized":[26],"by":[27,101,183,210],"optimizing":[28],"the":[29,56,87,111,122,140,145,157,171,175,178,185,195,199,204],"Ginzburg-Landau":[30,196],"functional":[31,107,197],"-":[32,41,164],"a":[33,44,92,129,134,161,166],"ubiquitous":[34],"model":[35],"in":[36],"physics":[37],"and":[38,67,82,95,117,148,216,225],"differential":[39],"geometry":[40],"leading":[42],"to":[43,73,80,84,120,193,212,232],"simple":[45],"algorithm":[46,88],"for":[47],"computing":[48],"bijective":[49,93],"correspondences":[50,99],"using":[51],"only":[52],"standard":[53],"tools":[54],"tangent":[57],"vector":[58],"field":[59],"toolbox.":[60],"method":[62,209],"avoids":[63],"combinatorial":[64],"mesh":[65],"modifications":[66],"does":[68,89],"not":[69,90],"require":[70],"barrier":[71],"functions":[72],"enforce":[74,233],"bijectivity":[75],"making":[76],"it":[77],"more":[78],"robust":[79],"noise":[81],"simpler":[83],"implement.":[85],"Moreover,":[86],"assume":[91],"initialization":[94],"untangle":[97],"non-bijective":[98],"generated":[100],"computationally":[102],"cheaper":[103],"methods":[104],"such":[105],"as":[106,156],"maps.":[108],"It":[109],"supports":[110,227],"use":[112],"both":[114],"landmark":[115,118],"points":[116],"curves":[119],"guide":[121],"correspondence.":[123],"key":[125],"idea":[126],"is":[127],"that":[128,218,229],"bijection":[130],"defines":[133],"two-dimensional":[135],"mapping":[136,150,189],"surface":[137,151],"sitting":[138],"inside":[139],"four-dimensional":[141],"product":[142,172],"space":[143],"two":[146],"inputs,":[147],"this":[149,188],"stored":[154],"implicitly":[155],"set":[159],"complex":[162,167,200],"section":[163],"essentially":[165],"function":[168],"defined":[169],"on":[170],"space.":[173],"Now":[174],"map":[179,236],"optimized":[182],"minimizing":[184,194],"area":[186],"surface,":[190],"which":[191],"amounts":[192],"section.":[201],"demonstrate":[203],"practical":[205],"benefits":[206],"our":[208,219],"comparing":[211],"state-of-the-art":[213],"correspondence":[214],"algorithms":[215],"show":[217],"offers":[222],"improved":[223],"stability":[224],"naturally":[226],"constraints":[228],"are":[230],"difficult":[231],"explicit":[235],"representations.":[237]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-06T00:00:00"}