We apply the Thom–Milnor theorem to obtain the upper bounds on the amount of isolated (1) critical points of a potential generated by several fixed point charges(Maxwell’s problem on point charges), (2) critical points of SINR, (3) critical points of a potential generated by several fixed Newtonian point masses augmented with a quadratic term, (4) central configurations in the n-body problem. In particular, we get an exponential bound for Maxwell’s problem and the polynomial bound for the case of an “even dimensional” potential in Maxwell’s problem.

中文翻译：

---

通过 Thom–Milnor 定理确定孤立临界点数量的上限

我们应用 Thom–Milnor 定理来获得孤立 (1) 由多个定点电荷产生的电势临界点（点电荷麦克斯韦问题）的数量上限，(2) SINR 临界点，(3)由几个固定的牛顿点质量生成的势的临界点，并用二次项增强，（4）n体问题中的中心配置。特别是，我们得到了麦克斯韦问题的指数界和麦克斯韦问题中“偶维”势情况的多项式界。