1 citations · 1 across the 9 of their papers we have counts for
9 papers
Ideal points, directed completion and the case of the maximally extended Schwarzschild spacetime
Nicola Gigli, Argam Ohanyan, Marco Picerni +2
We study the directed completion of Lorentzian pre-length spaces, and we show that, under some natural assumptions which cover the case of smooth globally hyperbolic spacetimes, it…
The many-body Blaschke-Santaló type inequality via optimal transport
Shibing Chen, Yuanyuan Li, Dongmeng Xi +1
Let be origin-symmetric measurable sets of finite volume such that \[ \sum_{1\le i<j\le k}\langle x_i,x_j\rangle\le \binom{k}{2}, \qquad \forall\…
The Mahler Conjecture in Three Dimensions
Shibing Chen, Yuanyuan Li, Dongmeng Xi +1
The Mahler conjecture dates back to 1938. This paper solves the conjecture for general convex bodies in three dimensions by developing a method called the shadow flow. The equality…
The Symmetric Mahler Inequality in Dimension Three via Admissible Shadow Systems
Shibing Chen, Yuanyuan Li, Dongmeng Xi +1
The three-dimensional symmetric Mahler inequality states that, for every origin-symmetric convex body \(K=-K\subset \mathbb{R}^3\), \[ \VP(K)= |K|\,|K^\circ|\geq \frac{32}{3}. \] I…
On a generalisation sum involving the Euler function
Zhaoxi Ye, Zhefeng Xu
Let , be real numbers and be the Euler function. In this paper, we study the asymptotical behaviour of the summation function $$S_{j,k}(x):=\sum_{n\le x}\fr…
Involves averaging arithmetic and integral partial functions over sparse set
Zhaoxi Ye, Zhefeng Xu
Let be a prime number, and be a class of arithmetic functions satisfying some simple conditions. In this short paper, we study the asymptotical behaviour of summat…