Uniqueness of sets of positive reach by curvature measures
A classical result in the theory of convex bodies (Schneider 1978)
asserts that if the \(k\)-th curvature measure of a convex body
\(C \subseteq \mathbf{R}^{n+1}\), for some \(k \in \{0, \ldots ,n-1\}\),
is proportional to the boundary area measure of \(C\), then \(C\) must be a round ball.
In a recent work, we have obtained a generalization of this result to sets
of positive reach (Hug-Santilli 2022). In this series of lectures,
we aim to discuss this result, along with some natural related questions.
