Regularity aspects of variational problems

该项目将调查一个或多个各种开放的问题，在正则性理论的极小子流形和相关领域。特别是，最近的事态发展，在分析分支点奇点的稳定最小超曲面，面积最小化（积分和模p）电流和多值调和函数产生了一个重要的循环的新思想和技术。因此，这些发展开辟了进一步发展的可能性，如扩展到边界的各种内部正则性理论，和潜在的应用程序的方法，各种偏微分方程的问题。博士项目最终将涉及这些问题的某些方面，在最初的一段时间后，候选人将被要求获得解决这些规律性问题所需的大量几何测量理论背景。

The project will investigate one or more of the various open questions in the regularity theory of minimal submanifolds and related areas. In particular, recent developments in the analysis of branch point singularities of stable minimal hypersurfaces, area minimising (integral and mod p) currents and multi-valued harmonic functions have generated an important circle of new ideas and techniques. These developments have thus opened up possibilities for further progress, such as extending the various interior regularity theories to the boundary, and potential applications of the methods to various PDE problems. The PhD project will eventually involve some aspect of these questions, after an initial period of time in which the candidate will be required to aquire the substantial Goemetric Measure Theory background necessary to tackle these regularity questions.