Moduli Spaces of Properly Embedded Minimal Surfaces

June 6 to June 10, 2005

at the

American Institute of Mathematics, Palo Alto, California

organized by

Michael Wolf, David Hoffman, and Matthias Weber

Original Announcement

This workshop will be devoted to advancing the understanding of properly embedded minimal surfaces in three-space, a subject whose roots to go back to Euler and Lagrange. New examples discovered in an explosion of activity in the 1980's have gradually focused the subject on the problem of classification. Recently, several new approaches and techniques have been developed which together begin to suggest that it might be possible to organize these examples into families, and indeed to describe the structure of the space of properly embedded minimal surfaces. In particular, dramatic advances have been made towards the goal of characterizing the classical surfaces as the unique examples with fundamental properties, and new families of examples have been found that were either unexpected or thought to be unapproachable. This workshop will be tightly focused on a few specific questions which are fundamental for this classification effort. These problems are linked by a confluence of attention from mathematicians with different points of view and by the prospect that real progress might be made by approaches using several different methods simultaneously.

The main topics of the workshop are:

  1. Existence of new properly embedded minimal surfaces of finite topology;
  2. The uniqueness question for classical minimal surfaces, Scherk's surface and the Riemann example in particular;
  3. The existence question for properly embedded minimal surfaces with infinite topology but no finite topology quotient;
  4. Deformations of properly embedded minimal surfaces and limits of families of such surfaces.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.