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math.DG2008
Triply Periodic Minimal Surfaces Bounded by Vertical Symmetry Planes
Shoichi Fujimori, Matthias Weber
We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a Schwarz-Christoffel formula for periodic polygo…
math.DG1998
Minimal Surfaces of Least Total Curvature and Moduli Spaces of Plane Polygonal Arcs
Matthias Weber, Michael Wolf
We prove the existence of complete minimal surfaces of genus g>1 which minimize the total curvature for their genus. Our method is first to identify this (Weierstrass high dimensio…