Related papers: Rotation equivariant Minkowski valuations

The rho-invariant is an invariant of odd-dimensional manifolds with finite fundamental group, and lies in the representations modulo the regular representations (after tensoring with Q). It is a fundamental invariant that occurs in…

Volume polynomials measure the growth of Minkowski sums of convex bodies and of tensor powers of positive line bundles on projective varieties. We show that Aluffi's covolume polynomials are precisely the polynomial differential operators…

One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…

We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing…

We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a…

We define an equivariant index of Spin$^c$-Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. The main result in this paper is that the index decomposes into irreducible representations according to…

We show that every hypercyclic operator on a real locally convex space admits a dense, invariant linear manifold of hypercyclic vectors.

It is well known that Rubik's cube has a set of group invariants. These values do not change if any layer was rotated, but they can change in case if some of the cubes were removed from the puzzle, mixed up and returned back. In this paper,…

We study the iterations of a class of curvature image operators $\Lambda_p^{\varphi}$ introduced by the author in (J. Funct. Anal. 271 (2016) 2133--2165). The fixed points of these operators are the solutions of the $L_p$ Minkowski problems…

Equivariance has emerged as a desirable property of representations of objects subject to identity-preserving transformations that constitute a group, such as translations and rotations. However, the expressivity of a representation…

A new class of continuous valuations on the space of convex functions on $\mathbb{R}^n$ is introduced. On smooth convex functions, they are defined for $i=0,\dots,n$ by \begin{equation*} u\mapsto \int_{\mathbb{R}^n} \zeta(u(x),x,\nabla…

We give a min-max characterization of the weighted Dirac eigenvalues, and show that the weighted eigenvalues and eigenspaces of Dirac operators are continuous with respect to weak $L^p$ convergence of the inverse weight, for any $p>n$.…

Let ${\mathcal Q}_n^d$ be the vector space of forms of degree $d\ge 3$ on ${\mathbb C}^n$, with $n\ge 2$. The object of our study is the map $\Phi$, introduced in papers [EI], [AI1], that assigns every nondegenerate form in ${\mathcal…

Let $X=(X(n))_{n \in \mathbb{Z_+}}$ be a standard subproduct system of $C^*$-correspondences over a $C^*$-algebra $\mathcal M.$ Assume $T=(T_n)_{n \in \mathbb{Z_+}}$ to be a pure completely contractive, covariant representation of $X$ on a…

In this paper, we investigate the log-concavity property of the first eigenfunction to the weighted $p$-Laplace operator in class of bounded, convex and smooth domain. Moreover, we prove a Brunn-Minkowski-type inequality for the first…

We consider spacelike surfaces in the four-dimensional Minkowski space and introduce geometrically an invariant linear map of Weingarten-type in the tangent plane at any point of the surface under consideration. This allows us to introduce…

A well-known result says that the Euclidean unit ball is the unique fixed point of the polarity operator. This result implies that if, in $\mathbb{R}^n$, the unit ball of some norm is equal to the unit ball of the dual norm, then the norm…

Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations…

We express all equivariant Gromov-Witten invariants of the projective line as matrix elements of explicit operators acting in the Fock space. As a consequence, we prove the equivariant theory is governed by the 2-Toda hierarchy of Ueno and…

We revisit a classical theme of (general or translation invariant) valuations on convex polyhedra. Our setting generalizes the classical one, in a ``dual'' direction to previously considered generalizations: while previous research was…