Zobrazeno 1 - 10
of 11 417
pro vyhledávání: '"P. Blaschke"'
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:
Milman, Emanuel, Yehudayoff, Amir
The Blaschke-Santal\'o inequality states that the volume product $|K| \cdot |K^o|$ of a symmetric convex body $K \subset \mathbb{R}^n$ is maximized by the standard Euclidean unit-ball. Cordero-Erausquin asked whether the inequality remains true for a
Externí odkaz:
http://arxiv.org/abs/2410.21093
In this paper, we study new extensions of the functional Blaschke-Santalo inequalities, and explore applications of such new inequalities beyond the classical setting of the standard Gaussian measure.
Externí odkaz:
http://arxiv.org/abs/2409.11503
Autor:
Celik, Mehmet, Duguin, Mathis, Guo, Jia, Luo, Dianlun, Spinelli, Kamryn, Zeytuncu, Yunus E., Zhu, Zhuoyu
In 2021, Dan Reznik made a YouTube video demonstrating that power circles of Poncelet triangles have an invariant total area. He made a simulation based on this observation and put forward a few conjectures. One of these conjectures suggests that the
Externí odkaz:
http://arxiv.org/abs/2410.18863
Autor:
Kalaj, David
Let $\mathbb{D}$ be the unit disk in the complex plane. Among other results, we prove the following curious result for a finite Blaschke product: $$B(z)=e ^{is}\prod_{k=1}^d \frac{z-a_k}{1-z \overline{a_k}}.$$ The Lebesgue measure of the sublevel set
Externí odkaz:
http://arxiv.org/abs/2407.19539
Autor:
Li, Liulan, Ponnusamy, Saminthan
Consider the family of locally univalent analytic functions $h$ in the unit disk $|z|<1$ with the normalization $h(0)=0$, $h'(0)=1$ and satisfying the condition $${\real} \left( \frac{z h''(z)}{\alpha h'(z)}\right) <\frac{1}{2} ~\mbox{ for $z\in \ID$
Externí odkaz:
http://arxiv.org/abs/2407.14922
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Akademický článek
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Consider a uniformly distributed random linear subspace $L$ and a stochastically independent random affine subspace $E$ in $\mathbb{R}^n$, both of fixed dimension. For a natural class of distributions for $E$ we show that the intersection $L\cap E$ a
Externí odkaz:
http://arxiv.org/abs/2404.14253
Autor:
Drach, Kostiantyn
We generalize the classical Blaschke Rolling Theorem to convex domains in Riemannian manifolds of bounded sectional curvature and arbitrary dimension. Our results are sharp and, in this sharp form, are new even in the model spaces of constant curvatu
Externí odkaz:
http://arxiv.org/abs/2404.02739