论文标题
球体上的低能点和真实的投影平面
Low energy points on the sphere and the real projective plane
论文作者
论文摘要
我们在$ \ mathbb {s}^2 $上介绍了一个点的概括，钻石合奏，包含$ \ mathbb {s}^2 $上的$ n $点的集合，所有$ n \ in \ mathbb {n} $中的$ n \ ins $ n \ a的$ n \。我们将此构造扩展到真实的投影平面$ \ Mathbb {Rp}^2 $，并在最后一个空间上获得了绿色和对数能量的上限和下限。
We present a generalization of a family of points on $\mathbb{S}^2$, the Diamond ensemble, containing collections of $N$ points on $\mathbb{S}^2$ with very small logarithmic energy for all $N\in\mathbb{N}$. We extend this construction to the real projective plane $\mathbb{RP}^2$ and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space.
