Tensor valuations

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This project aims at a thorough study of integral geometric results and morphological properties of tensorial functionals of various classes of sets. One main focus will be on translative, kinematic and rotational integral geometric formulas for tensor valuations and for not necessarily additive tensor functionals. We will introduce tensor-valued functionals for quite general classes of sets and with respect to different generating measures. This will enable us to apply tensor valuations as morphological measures that are relevant to the physical processes in anisotropic microstructured materials, and for the thermodynamics of ensembles of non-spherical particles. Tensor functionals will play an important role as geometric descriptors in all projects of the proposal. A particular emphasis in this project will be on foundational problems.