MARSLAND , Stephen

A de Rham p-current can be viewed as a map (the current map) between the set of embeddings of a closed p-dimensional manifold into an ambient n-manifold and the set of linear functionals on differential p-forms. We demonstrate that, for suitably chosen Sobolev topologies on both the space of embeddings and the space of p-forms, the current map...

The Baker-Campbell-Hausdorff (BCH) formula links the Lie group and Lie algebra by giving a formula for group multiplication of elements close to the identity in terms of the Lie bracket. This has applications in geometry, algebra, and partial differential equations, and provides simple proofs of further developments of Lie theory. To date,...

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These are the proceedings of the workshop "Math in the Black Forest", which brought together researchers in shape analysis to discuss promising new directions. Shape analysis is an inter-disciplinary area of research with theoretical foundations in infinite-dimensional Riemannian geometry, geometric statistics, and geometric stochastics, and...