L p -versions of generalized Korn inequalities for incompatible tensor fields in arbitrary dimensions with p-integrable exterior derivative

Functional versions of L p - affine surface area and entropy inequalities . ∗

In contemporary convex geometry, the rapidly developing Lp-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the Lp-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original Lp-affi...

Actions for spinor fields in arbitrary dimensions

We are going to give a systematic presentation of spinors in various spacetime dimensions which is a prerequisite for understanding the supersymmetry. (For general reviews see [1,2,3].) To set up the conventions, we will consider in what follows the Dirac matrices that satisfy the following Clifford algebra {γ, γ} = 2η1 , η = diag(+ · · ·+,− · · ·−) , (1) the sign +, − appear t, s times which a...

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

New L P Affine Isoperimetric Inequalities *

We prove new Lp affine isoperimetric inequalities for all p ∈ [−∞, 1). We establish, for all p 6= −n, a duality formula which shows that Lp affine surface area of a convex body K equals Ln2 p affine surface area of the polar body K◦.

The Formula of Grangeat for Tensor Fields of Arbitrary Order in n Dimensions

The cone beam transform of a tensor field of order m in n >/= 2 dimensions is considered. We prove that the image of a tensor field under this transform is related to a derivative of the n-dimensional Radon transform applied to a projection of the tensor field. Actually the relation we show reduces for m = 0 and n = 3 to the well-known formula of Grangeat. In that sense, the paper contains a ge...