Resumen de Flat structures and the triply periodic minimal surfaces C(H) and tC(P)

Robert Huff

• The C(H) and tC(P) surfaces are one-parameter families of embedded, triply periodic minimal surfaces, with the former derived by A. Schoen and the latter derived by Fischer and Koch. Existence proofs of these surfaces using the conjugate Plateau method have been given by Karcher. In this paper, an alternative proof is presented using flat structures on the surfaces. This proof uses a different fundamental region than Karcher, and the geometry of this region makes clear a network of straight lines on the surfaces.