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Explore the concept of smooth valuations on manifolds in this 39-minute lecture by Dima Faifman at the Hausdorff Center for Mathematics. Learn how smooth valuations generalize from convex sets to manifolds and discover the method of obtaining them through restriction of translation-invariant smooth valuations in higher-dimensional linear spaces. Examine the existence of Crofton formulas for all smooth valuations on manifolds and investigate a related problem involving finite families of subspaces, revealing an unexpected flexibility property of translation-invariant valuations. Gain insights from this joint work with Georg Hofstaetter, which addresses the Nash problem for smooth valuations and its implications in geometric measure theory.
