Anisotropic lower-dimensional Minkowski content and S-content

This paper investigates the lower-dimensional anisotropic Minkowski content and S-content. We establish that these anisotropic contents exhibit properties analogous to their isotropic counterparts by proving analogous inequalities between the lower-dimensional anisotropic Minkowski content and S-content S-content. A key component of our approach is demonstrating that the associated anisotropic volume function is of Kneser type, a result that underpins many of our proofs. In addition, we introduce anisotropic versions of the Minkowski and S-dimensions and derive inequalities relating them. As an application, we analyze the existence of the log₂(3)-dimensional anisotropic Minkowski and S-contents of the Sierpinski gasket.