论文标题
双曲线能量最小化，赫奇 - 塞格质量中心的良好性
Well-posedness of Hersch-Szegő's center of mass by hyperbolic energy minimization
论文作者
论文摘要
相对于径向增加的重量，有限测量的质量中心表明存在，是唯一的，并且不断依赖于该度量。通过将质量中心表征为严格沿双曲线测量学凸的能量功能的最小点来扩展这种类型的结果。一个特殊的案例是赫奇（Hersch）在球体上的大规模引理中心，它是由于杜迪（Douady）和厄尔（Earle）引入的对数内核的凸性。
The hyperbolic center of mass of a finite measure on the unit ball with respect to a radially increasing weight is shown to exist, be unique, and depend continuously on the measure. Prior results of this type are extended by characterizing the center of mass as the minimum point of an energy functional that is strictly convex along hyperbolic geodesics. A special case is Hersch's center of mass lemma on the sphere, which follows from convexity of a logarithmic kernel introduced by Douady and Earle.
