3 citations · 4 across the 12 of their papers we have counts for
14 papers
Minimal covering bodies and Brunn-Minkowski type inequalities for the covering radius
Giulia Codenotti, Ansgar Freyer, Katarina Krivokuća
Inclusion minimal convex bodies with the property that the integer translates of cover the space are studied. Such bodies are referred to as minimal covering bodies and it…
Exact Flatness Constant for One-Point Convex Bodies and the Discrete Isominwidth Problem: The Planar Case
Gennadiy Averkov, Giulia Codenotti, Ansgar Freyer +1
A variant of the flatness problem from integer programming is studied, in which one considers convex bodies in with at most interior lattice points. The maximum…
Exponential valuations on lattice polygons valued at formal power series
Karoly J. Boroczky, Matyas Domokos, Ansgar Freyer +2
We classify valuations on lattice polygons with values in the ring of formal power series that commute with the action of the affine unimodular group. A typical example of such val…
The canonical form, scissors congruence and adjoint degrees of polytopes
Tom Baumbach, Ansgar Freyer, Julian Weigert +1
We study the canonical form as a valuation in the context of scissors congruence for polytopes. We identify the degree of its numerator - the adjoint polynomial $\operatorname{…
Pal's isominwidth problem in the hyperbolic space
Karoly J. Boroczky, Ansgar Freyer, Adam Sagmeister
The paper focuses on possible hyperbolic versions of the classical Pal isominwidth inequality in R^2 from 1921, which states that for a fixed minimal width, the regular triangle ha…
The isominwidth problem on the 2-sphere
Ansgar Freyer, Ádám Sagmeister
Pál's isominwidth theorem states that for a fixed minimal width, the regular triangle has minimal area. A spherical version of this theorem was proven by Bezdek and Blekherman, if…
Exponential valuations on lattice polygons
Karoly J. Boroczky, Matyas Domokos, Ansgar Freyer +3
We classify translatively exponential and GL(2,Z) covariant valuations on lattice polygons valued at measurable real functions. A typical example of such valuations is induced by t…
Unimodular Valuations beyond Ehrhart
Ansgar Freyer, Monika Ludwig, Martin Rubey
A complete classification of unimodular valuations on the set of lattice polygons with values in the spaces of polynomials and formal power series, respectively, is established. Th…
The affine subspace concentration inequality for centered convex bodies
Katharina Eller, Ansgar Freyer
An affine version of the linear subspace concentration inequality as proposed by Wu is established for centered convex bodies. This generalizes results from Wu and Freyer, Henk, Ki…
Lattice Reduced and Complete Convex Bodies
Giulia Codenotti, Ansgar Freyer
The purpose of this paper is to study convex bodies for which there exists no convex body of the same lattice width. Such bodies shall be called ``lattic…
Polynomial Bounds in Koldobsky's Discrete Slicing Problem
Ansgar Freyer, Martin Henk
In 2013, Koldobsky posed the problem to find a constant , depending only on the dimension , such that for any origin-symmetric convex body there exis…
Affine Subspace Concentration Conditions for Centered Polytopes
Ansgar Freyer, Martin Henk, Christian Kipp
Recently, K.-Y. Wu introduced affine subspace concentration conditions for the cone volumes of polytopes and proved that the cone volumes of centered, reflexive, smooth lattice pol…
Interpolating between volume and lattice point enumerator with successive minima
Ansgar Freyer, Eduardo Lucas
We study inequalities that simultaneously relate the number of lattice points, the volume and the successive minima of a convex body to one another. One main ingredient in order to…
Bounds on the lattice point enumerator via slices and projections
Ansgar Freyer, Martin Henk
Gardner, Gronchi and Zong posed the problem to find a discrete analogue of M. Meyer's inequality bounding the volume of a convex body from below by the geometric mean of the volume…