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Using a representation of curves and surfaces via differential forms on the ambient space, we reformulate this problem as a convex optimization. This change of variables overcomes many difficulties in previous numerical attempts and allows us to find the global minimum across all possible surface topologies. The new algorithm is based on differential forms on the ambient space and does not require handling meshes. We adopt the Alternating Direction Method of Multiplier (ADMM) to find global minimal surfaces. The resulting algorithm is simple and efficient: it boils down to an alternation between a Fast Fourier Transform (FFT) and a pointwise shrinkage operation. We also show other applications of our solver in geometry processing such as surface reconstruction.<\/jats:p>","DOI":"10.1145\/3450626.3459781","type":"journal-article","created":{"date-parts":[[2021,7,20]],"date-time":"2021-07-20T00:04:27Z","timestamp":1626739467000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":19,"title":["Computing minimal surfaces with differential forms"],"prefix":"10.1145","volume":"40","author":[{"given":"Stephanie","family":"Wang","sequence":"first","affiliation":[{"name":"University of California"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Albert","family":"Chern","sequence":"additional","affiliation":[{"name":"University of California"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2021,7,19]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Touching Soap Films","author":"Arnez Andreas","unstructured":"Andreas Arnez , Konrad Polthier , Martin Steffens , and Christian Teitzel . 2007. 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