Nicholas Korevaar will continue his work on surfaces of constant mean curvature in three dimensional space. Historically most research was directed at surfaces of zero mean curvature, these are known as minimal surfaces. Prototypical examples being soap films. During the last five years there has been a great deal of activity in the realm of non-zero mean curvature; here soap bubbles are the typical examples. This work received its impetus from Wente's counterexample to the Hopf conjecture. During the last year Kapouleas has shown how to construct many more such examples of different topological types. Korevaar's work is in many ways complementary to this and a natural development in the sense that he is looking at the structure that such surfaces must have rather than attempting to construct more examples. Korevaar's earlier work with his collaborators has led to a good understanding of the behaviour of these surfaces near to infinity. His attention will now turn to an investigation of the structure in bounded regions of space. This will involve an interaction of ideas from geometry and the theory of partial differential equations. He will also carry out related research into capillarity questions and into convexity theorems for solutions of elliptic equations.
