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The distortion of these maps can easily be minimized by optimizing the Ginzburg-Landau functional\u2014a ubiquitous model in physics and differential geometry\u2014leading to a simple algorithm for computing bijective correspondences using only standard tools of the tangent vector field toolbox. The method avoids combinatorial mesh modifications and does not require barrier functions to enforce bijectivity making it more robust to noise and simpler to implement. Moreover, the algorithm does not assume a bijective initialization and can untangle non-bijective correspondences generated by computationally cheaper methods such as functional maps. It supports the use of both landmark points and landmark curves to guide the correspondence. The key idea is that a bijection between surfaces defines a two-dimensional mapping surface sitting inside the four-dimensional product space of the two inputs, and this mapping surface can be stored implicitly as the zero set of a\n                    <jats:italic toggle=\"yes\">complex section<\/jats:italic>\n                    \u2014essentially a complex function defined on the product space. Now the distortion of the map can be optimized by minimizing the area of this mapping surface, which amounts to minimizing the Ginzburg-Landau functional of the complex section. We demonstrate the practical benefits of our method by comparing to state-of-the-art correspondence algorithms and show that our implicit representation offers improved stability and naturally supports constraints that are difficult to enforce with explicit map representations.\n                  <\/jats:p>","DOI":"10.1145\/3811368","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Implicit Minimal Surfaces for Bijective Correspondences"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-9401-2362","authenticated-orcid":false,"given":"Etienne","family":"Corman","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, Nancy, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4023-5026","authenticated-orcid":false,"given":"Yousuf","family":"Soliman","sequence":"additional","affiliation":[{"name":"Side Effects Software Inc, Los Angeles, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2192-411X","authenticated-orcid":false,"given":"Robin","family":"Magnet","sequence":"additional","affiliation":[{"name":"Inria, Paris, France"},{"name":"Universit\u00e9 Paris Cit\u00e9, Paris, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-5645-9636","authenticated-orcid":false,"given":"Mark","family":"Gillespie","sequence":"additional","affiliation":[{"name":"Inria, Salt Lake City, USA"},{"name":"University of Utah, Salt Lake City, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3572897"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-7824(00)01180-6"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073615"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/2816795.2818099"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982412"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601158"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766921"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2005.54.2601"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.70208"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13503"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1023\/B:VISI.0000043755.93987.aa"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-007-9006-1"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/3757377.3763976"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-023-01933-1"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201276"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01761.x"},{"key":"e_1_2_2_17_1","volume-title":"The regularity of minimal surfaces in higher codimension. 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