Minimal submanifolds and related problems (07w5059)
A 5-day workshop in the summer of 2007 at BIRS on
\"Minimal submanifolds and related problems\" is needed to stimulate
the classical yet also modern mathematical field of minimal submanifolds.
The workshop will focus on recent developments on minimal surfaces in
3-dimensional space and minimal submanifolds of high co-dimension
such as special Lagrangian submanifolds, more general calibrated
submanifolds, and J-holomorphic curves. It will also include applications
in general relativity and string theory. For instance, in relativity there
is interest in dynamical horizons which are 3-dimensional spacelike
hypersurfaces foliated by apparent horizons in a slicing of a
spacetime. Apparent horizons are minimal 2-spheres in some cases, but
usually solutions of a prescribed mean curvature equation of a particular
type. There is also interest in higher dimensional black holes
which is related to string theory.
In recent years, progress has been made on the high co-dimension
minimal submanifold theory. Calibrated geometry, a subfield of minimal
submanifolds, also witnessed a new wave of insights. Naturally the
progress found many applications to the related \"physical\" fields.
The partial differential equations which govern calibrated minimal
submanifolds, such as the special Lagrangian equations, are usually
fully nonlinear ones. It is important to understand properties of these
equations, so the workshop will have a substantial component in nonlinear