发表机构
Chern Institute of Mathematics & LPMC, Nankai University（南开大学陈省身数学研究所与LPMC）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究平面五体问题中带一个主导质量的严格凸中心构型，证明在卫星总质量比满足单一上界时，对任意指定顺序，构型存在且唯一，并通过共轨极限与碰撞极限的延拓建立该结果。
AI 中文摘要
我们研究了平面牛顿五体问题中具有一个主导质量和四个任意正质量卫星的严格凸中心构型。我们证明，对卫星与主星总质量比的单一正上界，可保证在凸包上五个体的每个指定有向顺序下，构型的存在性和唯一性（在平移、旋转和正缩放意义下）。该上界独立于所有卫星质量比，包括任意接近质量单纯形边界的比值。约束Hessian在六维形状空间上是非退化的。我们首先通过角Hessian估计证明凸共轨极限的唯一性和非退化性。然后，随着卫星质量比变化，我们对可能的碰撞极限进行分类，并为对、三体及三体内的对构造正则化局部延拓。有向面积的精确分解在独立参数邻域上保持严格凸性。这些延拓将每个足够小质量的构型连接到唯一的共轨构型，并得出公共上界。
英文摘要
We study strictly convex central configurations of the planar Newtonian five-body problem with one dominant mass and four satellites of arbitrary positive masses. We prove that a single positive bound on the total satellite-to-primary mass ratio guarantees existence and uniqueness for every prescribed directed order of the five bodies on the convex hull, up to translations, rotations and positive scaling. The bound is independent of all satellite mass ratios, including ratios arbitrarily close to the boundary of the mass simplex. The constrained Hessian is nondegenerate on the six-dimensional shape space. We first prove uniqueness and nondegeneracy for the convex coorbital limit by an angular Hessian estimate. We then classify the possible collision limits as the satellite mass ratios vary and construct regularized local continuations for pairs, triples and pairs within triples. An exact factorization of the signed areas preserves strict convexity on independent parameter neighborhoods. These continuations connect every sufficiently small-mass configuration to the unique coorbital configuration and yield the common bound.
