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# Bernig, A (2003). Scalar curvature of definable CAT-spaces. Advances in Geometry, 3(1):23-43.

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## Abstract

We study the scalar curvature measure for sets belonging to o-minimal structures (e.g. semialgebraic or subanalytic sets) from the viewpoint of metric dierential geometry. Theorem: Let S be a compact connected definable pseudo-manifold with curvature bounded from above, then the singular part of the scalar curvature measure is non-positive. The topo- logical restrictions cannot be removed, as is shown in examples.