\[\newcommand{\vol}{\text{Vol}}\] (This is a summary of my study during the Spring semester of my first year at Ulm) Introduction Let \(r > 0\), denote \(B(p, r)\) the ball of radius \(r > 0\) centered at \(p\). onsider the space \(\mathbb{R}^n\), a sphere packing configuration is a set of points \(\mathcal{P} \subsetneq \mathbb{R}^n\) ... 10 Sep 2024 - 13 minute read
Li’s discrete reductions Let us focus on Li’s proof for dimension \(n \in \{3, 4, 5\}\) (Li, 2022). A function \(f : \mathbb{R}^n \to \mathbb{R}\) is called an auxiliary function if it is smooth, and satisfies the following conditions. $f(x) = O\left(\frac{1}{(1 + |x|)^k}\right)$ for all \(k\), \(f(0) > 0\), \(\widehat{f}(0) \geq 1\),... 10 Sep 2024 - 6 minute read