论文标题
最小化的运动方案，用于紧凑的Riemannian歧管上的内在聚集
Minimizing movement scheme for intrinsic aggregation on compact Riemannian manifolds
论文作者
论文摘要
最近，已经研究了采用不同技术的紧凑型riemannian歧管上的聚合方程解决方案。这项工作证明了针对适当定期内在电势的测量值解决方案的存在。主要工具是使用最小化运动方案，该方案与最佳条件一起产生有限的传播速度。主要的技术难度是在切割基因座中的电势的非差异性，该电位通过最小化移动方案的测量插值的传播特性而解决，并且随着时间步长为零，并将其传递到极限。
Recently solutions to the aggregation equation on compact Riemannian Manifolds have been studied with different techniques. This work demonstrates the small time existence of measure-valued solutions for suitably regular intrinsic potentials. The main tool is the use of the minimizing movement scheme which together with the optimality conditions yield a finite speed of propagation. The main technical difficulty is non-differentiability of the potential in the cut locus which is resolved via the propagation properties of geodesic interpolations of the minimizing movement scheme and passes to the limit as the time step goes to zero.
