Intrinsic volumes on pseudo-Riemannian manifolds

Abstract: The intrinsic volumes in Euclidean space can be defined via Steiner's tube formula and were characterized by Hadwiger as the unique continuous, translation and rotation invariant valuations. By the Weyl principle, their extension to Riemannian manifolds behaves naturally under isometric embeddings.

In a series of papers with Dmitry Faifman and Gil Solanes, we developed a theory of intrinsic volumes in pseudo-Euclidean spaces and on pseudo-Riemannian manifolds. Fundamental results like Hadwiger's theorem, Weyl's principle and Crofton formulas on spheres have their natural analogues in the pseudo-Riemannian setting.

differential geometryfunctional analysis

Audience: researchers in the discipline

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Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

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