2013/09/16 by Daniel Hug, Hug, Daniel, Rolf Schneider +1 · 1 citation
Mathematics · Physics and Astronomy · #52A20 #52A22 #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1309.3998
openalex publication_date 2013/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant Minkowski tensors that were introduced by McMullen and characterized by Alesker. In analogy to the characterization theorems of Hadwiger and Alesker, we give here a complete classification of all locally defined tensor measures on convex bodies that share with the local Minkowski tensors the basic geometric properties of isometry covariance and weak continuity.