Appears in collection : 2026 - T1 - WS2 - Bridging visualization and understanding in Geometry and Topology

Minimal and constant mean curvature (CMC) surfaces in space forms -- $\mathbb R^3$, $\mathbb S^3$ or $\mathbb H^3$ -- can be represented in terms of holomorphic data. For minimal surfaces in $\mathbb R^3$, this is the classical Weierstrass Representation. In the other cases, this is usually called the Dorfmeister Pedit Wu (DPW) method. These representations can be implemented to produce pictures.

In this talk, I will present two theorems and the pictures that led to them. The first one is the existence of an embedded minimal surface in euclidean surface with finite topology and no symmetry at all. The second one is a recent counterexample to a conjecture about the isoperimetric problem. A recurent question is the following: is a picture a proof?