Gluing Delaunay ends to minimal n-noids using the DPW method

We construct constant mean curvature surfaces in euclidean space by gluing n half Delaunay surfaces to a non-degenerate minimal n-noid, using the DPW method.Comment: Includes a detailed proof of Alexandrov embeddednes

A minimal surface with unbounded curvature

We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.Comment: 24 pages, 2 figure

Opening infinitely many nodes

We develop a theory of holomorphic differentials on a certain class of non-compact Riemann surfaces obtained by opening infinitely many nodes.Comment: 21 pages, 1 figur

On the genus of triply periodic minimal surfaces

International audienceWe prove the existence of embedded minimal surfaces of arbitrary genus at least 3 in any flat 3-torus. In fact we construct a sequence of such surfaces converging to a planar foliation of the 3-torus. In particular, the area of the surface can be chosen arbitrarily large

On minimal surfaces bounded by two convex curves in parallel planes

International audienceWe prove that a compact minimal surface bounded by two closed convexe curves in parallel planes close enough to each other must be topologically an annulus