Singularity Behavior in Some Geometric Variational Problems

9704367 Hardt这个项目位于几何变分的一般领域，处理奇点和各种能量临界对象的行为。一些具体的研究集中在n-调和映射和双调和映射，带边界的极小曲面的正则性理论，以及簇中的等周和Sobolev不等式。地电变分涉及满足一组共同约束的对象族中各种极值和/或最优对象的问题。面积和能量最小化曲面是该理论研究的对象之一。这些表面在材料科学中有应用，因为它们可以用来模拟凝聚态物质。

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.