Geometric Problems and Special PDEs

我们想继续我们的两个相关项目——扩展我们的新方法来得到全局唯一性的结果——继续我们对子流形类的系统研究，特别是在空间形式中，在复射影空间中，在与某些类偏微分方程相关的仿射空间中，——进一步发展一种新的任意余维的Blaschke几何方法，——研究二次曲面中超曲面的极性等特殊情况，-继续研究与几何问题有关的高阶偏微分方程的解，-继续研究子流形的变分问题。我们的计划包括与我们的中国合作伙伴和进一步的客座研究人员的合作。此外，我们希望继续在北京和成都组织国际会议，以加强科学和国际合作，以及他们的几何小组及其相关伙伴作为卓越中心的声誉，并在柏林工业大学举办小型研讨会。

We want to continue our two linked projects to - extend our new methods for global uniqueness results - continue our systematic investigations on classes of submanifolds, in particular in space forms, in complex projective space, and in affine space in connection with certain classes of PDEs, - further develop a new approach of a Blaschke geometry of arbitrary codimension, - study special situations like polarity of hypersurfaces in quadrics, - proceed with the solutions of higher order PDEs which are related to geometric problems, - proceed with the investigation of variational problems for submanifolds. Our plans include the cooperation with our Chinese partners and further guest researchers. Moreover, we want to continue to organize international conferences at Beijing and Chengdu, to strengthen the scientific and international cooperation and reputation of their geometry groups and their associated partners as centers of excellence, as well as smaller workshops at the TU Berlin.