9704367 Hardt This project lies in the general area of geometric variational calculus, dealing with the behavior of singularities and various energy critical objects. Some specific investigations focus on n-harmonic maps and biharmonic maps, regularity theory for minimal surfaces with boundary, and isoperimetric and sobolev inequalities in varieties. Geoemtric variational calculus involves questions about various extremal and/or optimal objects amongst families of objects satisfying a common set of constraints. Area and energy minimizing surfaces are among the objects studied in this theory. These surfaces have applications in materials science as they can be used to model condensed matter.
