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pro vyhledávání: '"52A10"'
Autor:
Bogosel, Beniamin
The sensitivity of the areas of Reuleaux polygons and disk polygons is computed with respect to vertex perturbations. Computations are completed for both constrained and Lagrangian formulations and they imply that the only critical Reuleaux polygons
Externí odkaz:
http://arxiv.org/abs/2412.13808
Autor:
Haddad, J.
The radial mean bodies of parameter $p>-1$ of a convex body $K \subseteq \mathbb R^n$ are radial sets introduced in [4] by Gardner and Zhang. They are known to be convex for $p\geq 0$. We prove that if $K \subseteq \mathbb R^2$ is a convex body, then
Externí odkaz:
http://arxiv.org/abs/2412.01475
Autor:
Baek, Jineon
We resolve the moving sofa problem by showing that Gerver's construction with 18 curve sections attains the maximum area $2.2195\cdots$.
Comment: 119 pages, 21 figures
Comment: 119 pages, 21 figures
Externí odkaz:
http://arxiv.org/abs/2411.19826
The higher-rank numerical range is a convex compact set generalizing the classical numerical range of a square complex matrix, first appearing in the study of quantum error correction. We will discuss some of the real algebraic and convex geometry of
Externí odkaz:
http://arxiv.org/abs/2410.21625
Autor:
Datta, Basudeb, Gupta, Subhojoy
It is a classical fact in Euclidean geometry that the regular polygon maximizes area amongst polygons of the same perimeter and number of sides, and the analogue of this in non-Euclidean geometries has long been a folklore result. In this note, we pr
Externí odkaz:
http://arxiv.org/abs/2409.06529
Autor:
Cardó, Carles
The simplest way to generate a lattice of convex sets is to consider an initial set of points and draw segments, triangles, and any convex hull from it, then intersect them to obtain new points, and so forth. The result is an infinite lattice for mos
Externí odkaz:
http://arxiv.org/abs/2407.17210
In this paper, we give for the first time a systematic study of the variance of the distance to the boundary for arbitrary bounded convex domains in $\mathbb{R}^2$ and $\mathbb{R}^3$. In dimension two, we show that this function is strictly convex, w
Externí odkaz:
http://arxiv.org/abs/2407.12041
Autor:
Hughes, Gordon
There are multiple mappings that can be used to generate what we call the 'edge geometry' of a regular N-gon, but they are all based on piecewise isometries acting on the extended edges of N to form a 'singularity' set W. This singularity set is also
Externí odkaz:
http://arxiv.org/abs/2407.05937
Autor:
Borisenko, Alexander A.
In 1972, E. P. Senkin generalized the celebrated theorem of A. V. Pogorelov on unique determination of compact convex surfaces by their intrinsic metrics in the Euclidean 3-space $E^3$ to higher dimensional Euclidean spaces $E^{n+1}$ under a mild ass
Externí odkaz:
http://arxiv.org/abs/2406.15761
Autor:
Baek, Jineon
The moving sofa problem asks for the connected shape with the largest area $\mu_{\text{max}}$ that can move around the right-angled corner of a hallway $L$ with unit width. The best bounds currently known on $\mu_{\max}$ are summarized as $2.2195\ldo
Externí odkaz:
http://arxiv.org/abs/2406.10725