Geometric Problems and Special PDEs

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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.