Blaschke’s Inclusion Theorem
An extremely classical theorem from planar geometry is the following one: If \(B_1\) and \(B_2\) are two strictly convex, compact planar domains with smooth boundaries touching at some point \(p \in \partial B_1 \cap \partial B_2\) with common inner normal, then \(B_1 \subset B_2\) provided that the curvatures \(k_i(\nu)\) of the boundaries satisfy \(k_1(\nu) \ge … Continue reading "Blaschke’s Inclusion Theorem"