2010/01/14 by Peter Connor, Connor, Peter, Matthias Weber +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1001.2496
openalex publication_date 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using Traizet's regeneration method, we prove the existence of many new\n3-dimensional families of embedded, doubly periodic minimal surfaces. All these\nfamilies have a foliation of 3-dimensional Euclidean space by vertical planes\nas a limit. In the quotient, these limits can be realized conformally as noded\nRiemann surfaces, whose components are copies of C* with finitely many nodes.\nWe derive the balance equations for the location of the nodes and exhibit\nsolutions that allow for surfaces of arbitrarily large genus and number of ends\nin the quotient.\n