Geometric inequalities and equalities
Convex Geometry II. Distances and Measures, Approximation, Comparison and Symmetrisation

In n-dimensional Euclidean spaces ${ℝ}_2^n$ , there are so-called geometric inequalities and equalities linking several geometric quantities. Most of these were established in the 19th and especially 20th centuries .

Geometric inequalities and equalities are used in stereology (Stereologie), geometric tomography (Geometric Tomography), optimal control and partial differential equations (Optimal Control...