The principal investigator will continue his work on constrained variational problems, while at Rice University, as part of a group project based at the University of Minnesota (DMS-8718881). The specific problems to be addressed lie in the areas of harmonic mappings, geometric measure theory, partial differential equations, and mechanics. The principal investigator will study the regularity and singularity of solutions of minimizing, stationary, and dynamic problems. Constrained variational techniques will be used by the principal investigator to solve problems arising from the study of liquid crystals. Techniques for the solution of such problems date back to the eighteenth century with the invention of Lagrange Multipliers. This technique can be used to find the point on a surface which is farthest from a given point.
