论文标题
Hellinger-Kantorovich和球形Hellinger-Kantorovich空间的进化变化不平等现象
Evolutionary Variational Inequalities on the Hellinger-Kantorovich and Spherical Hellinger-Kantorovich spaces
论文作者
论文摘要
我们研究了在Hellinger-Kantorovich或Spherical Hellinger-Kantorovich空间上定义的地球半凸功能家族的最小化运动方案。通过利用这些空间的某些几何特性，我们证明，通过将最小化运动方案产生的点插值来产生的曲线序列会收敛到满足时间步骤时的进化变异不等式（EVI）的曲线。
We study the minimizing movement scheme for families of geodesically semi-convex functionals defined on either the Hellinger-Kantorovich or the Spherical Hellinger-Kantorovich space. By exploiting some of the finer geometric properties of those spaces, we prove that the sequence of curves, which are produced by geodesically interpolating the points generated by the minimizing movement scheme, converges to curves that satisfy the Evolutionary Variational Inequality (EVI), when the time step goes to 0.
