Gaussian Convex Bodies: a Nonasymptotic Approach
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-019-04256-3
Abstract: We study linear images of a symmetric convex body C ⊆ ℝN under an n × N Gaussian random matrix G, where N ≥ n. Special cases include common models of Gaussian random polytopes and… read more here.
Keywords: geometry; bodies nonasymptotic; nonasymptotic approach; gaussian convex ... See more keywords
On the heat content for the Poisson heat kernel over convex bodies
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.124655
Abstract: Abstract In this paper, the small time asymptotic behavior of the heat content related to the Poisson heat kernel over convex bodies of the euclidean space R d , d ≥ 2 , shall be… read more here.
Keywords: kernel convex; heat content; heat; heat kernel ... See more keywords
OpenGJK for C, C# and Matlab: Reliable solutions to distance queries between convex bodies in three-dimensional space
Sign Up to like & getrecommendations! Published in 2018 at "SoftwareX"
DOI: 10.1016/j.softx.2018.10.002
Abstract: Abstract Implementing a reliable algorithm for computing the distance between convex bodies is an involved and time-consuming task. Common applications of these algorithms include robot path planning, image rendering and collision detection. However, each application… read more here.
Keywords: distance; opengjk matlab; distance queries; queries convex ... See more keywords
A Characterization of the Polarity Mapping for Convex Bodies
Sign Up to like & getrecommendations! Published in 2023 at "Wuhan University Journal of Natural Sciences"
DOI: 10.1051/wujns/2023282093
Abstract: In this paper, we establish a characterization of the polarity mapping for 1-dimensional convex bodies, which is a supplement to the result for such a characterization obtained by Böröczky and Schneider. read more here.
Keywords: characterization polarity; polarity mapping; mapping convex; convex bodies ... See more keywords
A general slicing inequality for measures of convex bodies
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-019-2085-8
Abstract: AbstractWe consider the following inequality: μ(L)n−kn≤CkmaxH∈Grn−kμ(L∩H), $$\begin{aligned} \mu (L)^{\frac{n-k}{n}} \leq C^{k}\max_{H\in \mathit{Gr}_{n-k}}\mu (L \cap H), \end{aligned}$$ which is a variant of the notable slicing inequality in convex geometry, where L is an origin-symmetric star body… read more here.
Keywords: inequality; slicing inequality; general slicing; measures convex ... See more keywords
Some logarithmic Minkowski inequalities for nonsymmetric convex bodies and related problems
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-020-02314-y
Abstract: In this paper, we show the existence of a solution to an even logarithmic Minkowski problem for p -capacity and prove some analogue inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies involving… read more here.
Keywords: inequalities nonsymmetric; nonsymmetric convex; logarithmic minkowski; minkowski inequalities ... See more keywords
Estimations of Covering Functionals of Convex Bodies Based on Relaxation Algorithm
Sign Up to like & getrecommendations! Published in 2023 at "Mathematics"
DOI: 10.3390/math11092000
Abstract: Estimating covering functionals of convex bodies is an important part of Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a long-standing open problem from convex and discrete geometry. In this paper, we transform… read more here.
Keywords: functionals convex; estimations covering; covering functionals; algorithm ... See more keywords