Mark Meyer

activity

20232026

collaborators

8 papers

math.CA2026

Prescribed projections for a general class of maps and efficient covering by variable plane curves

Alan Chang, Robert Fraser, Alex McDonald +2

We prove a prescribed projection theorem for any class of non-linear projections defined on open subsets of the plane which satisfies some mild geometric conditions. This generaliz…

math.MG2026

Norm rigidity and equality cases for the Dyn--Farkhi inequality

Mark Meyer

For a convex body $K \subset R^{2}$ that is symmetric with respect to the origin, and for a nonempty set $S \subset R^{2}$ , we study the $K$ -Hausdorff distance from conve…

math.MG2026

L_p-Rogers--Shephard type inequalities for L_p-zonoids and symmetric bodies

Matthieu Fradelizi, Auttawich Manui, Mark Meyer +1

We study generalizations of the classical Rogers--Shephard inequalities in the framework of Firey $L_{p}$ -summation. We first consider the class of asymmetric $L_{p}$ -zonoids. In this…

math.MG2026

Equality cases for the $L_{p}$ -Rogers--Shephard inequality in the plane and for locally anti-blocking bodies in $R^{n}$

Matthieu Fradelizi, Auttawich Manui, Mark Meyer +1

The classical Rogers--Shephard inequalities were extended to the Firey $L_{p}$ -summation by Bianchini and Colesanti in the plane and by Zvavitch and the second and fourth authors for…

math.MG2026

A sharp $p$ -subadditive bound for the $l_{p}$ Hausdorff distance from convex hull

Mark Meyer

We study the $ℓ_{p}$ Hausdorff distance from convex hull, which for a compact set $A \subset R^{n}$ is defined by \begin{align*} d^{(\ell_p)}(A):=\sup_{x\in \text{conv}(A)}\…

math.MG2024

The Dyn-Farkhi conjecture and the convex hull of a sumset in two dimensions

Mark Meyer

For a compact set $A$ in $R^{n}$ the Hausdorff distance from $A$ to $conv (A)$ is defined by \begin{equation*} d(A):=\sup_{a\in\text{conv}(A)}\inf_{x\in A}|x-a|, \end{…

math.MG2024

Measuring the convexity of compact sumsets with the Schneider non-convexity index

Mark Meyer

In recent work, Franck Barthe and Mokshay Madiman introduced the concept of the Lyusternik region, denoted by $Λ_{n} (m)$ , to better understand volumes of sumsets. They gave a chara…

math.MG2023

Equality conditions for the fractional superadditive volume inequalities

Mark Meyer

While studying set function properties of Lebesgue measure, F. Barthe and M. Madiman proved that Lebesgue measure is fractionally superadditive on compact sets in $R^{n}$ . I…

Prescribed projections for a general class of maps and efficient covering by variable plane curves

Norm rigidity and equality cases for the Dyn--Farkhi inequality

L_p-Rogers--Shephard type inequalities for L_p-zonoids and symmetric bodies

Equality cases for the Lp​-Rogers--Shephard inequality in the plane and for locally anti-blocking bodies in Rn

A sharp p-subadditive bound for the lp​ Hausdorff distance from convex hull

The Dyn-Farkhi conjecture and the convex hull of a sumset in two dimensions

Measuring the convexity of compact sumsets with the Schneider non-convexity index

Equality conditions for the fractional superadditive volume inequalities

Equality cases for the $L_{p}$ -Rogers--Shephard inequality in the plane and for locally anti-blocking bodies in $R^{n}$

A sharp $p$ -subadditive bound for the $l_{p}$ Hausdorff distance from convex hull