黎曼流形上弱排斥相互作用能极小元的离散性
Discreteness of the minimizers of weakly repulsive interaction energies on Riemannian manifolds
摘要：
证明了在截面曲率有界的黎曼流形上极小化弱排斥能测度的支集不存在集中点。这扩展了Björck和Carrillo，Figalli和Patacchini在欧几里得空间上对这种能量的结果，并补充了Bilyk，Dai和Matzke关于球面上测地线Riesz能量极小的离散性的结果。
英文摘要：
It is shown that the supports of measures minimizing weakly repulsive energies on Riemannian manifolds with sectional curvature bounded below do not have concentration points. This extends the results of Björck and Carrillo, Figalli, and Patacchini for such energies on the Euclidean space, and complements the results about the discreteness of minimizers of the geodesic Riesz energy on the sphere by Bilyk, Dai, and Matzke.
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