A Geometric Characterization of Extremal Sets in ell_p Spaces

ℝ上的ℓ_p^n空间中球的极值超平面投影的稳定性

Stability of extremal hyperplane projections of balls in $\ell_p^n(\mathbb{R})$

该研究针对ℝ上的ℓ_p^n空间中单位球的中心超平面投影体积，证明了其稳定性估计，建立了Chasapis等人相关截面稳定性结果的对偶对应。

Davis' Convexity Theorem and Extremal Ellipsoids

We give a variety of uniqueness results for minimal ellipsoids circumscribing and maximal ellipsoids inscribed into a convex body. Uniqueness follows from a convexity or concavity criterion on the function used to measure the size of the ellipsoid. Simple examples with non-unique minimal or maximal ellipsoids conclude this article.

Rigidity of extremal quasiregularly elliptic manifolds

We show that for a closed $n$-manifold $N$ admitting a quasiregular mapping from the Euclidean $n$-space the following are equivalent: (1) order of growth of $π_1(N)$ is $n$, (2) $N$ is aspherical, and (3) $π_1(N)$ is virtually $\mathbb{Z}^n$ and torsion free.

A Note on Self-extremal Sets in $L_p(\Om)$ Spaces

We give a geometric characterization of self-extremal sets in $L_p(\Om)$ spaces that partially extends our previous results to the case of $L_p$\ spaces.

Geometric properties of extremal sets for the dimension comparison in Carnot groups of step 2

In Carnot groups of step 2 we consider sets having maximal or minimal possible homogeneous Hausdorff dimension compared to their Euclidean one: in the first case we prove that they must be in a sense vertical, that is a large part of these sets can lie off horizontal planes through their points, and in the latter case close to horizontal. The examples that had been used to prove the sharpness of the sub-Riemannian versus Euclidean dimension comparison intuitively satisfied these geometric properties, which we here quantify and prove to be necessary. We also show the sharpness of our statements…

极值几何中的锥优化

Conic optimization for extremal geometry

本文综述了锥优化在四种几何堆积问题（单位球面上的接吻数与可测π/2回避集，欧氏空间中的球堆积与可测一回避集）中的最新应用进展。