论文标题
在紧凑的歧管上切割基因座和变异不等式的均匀半腔估计值
Cut locus on compact manifolds and uniform semiconcavity estimates for a variational inequality
论文作者
论文摘要
我们研究一个紧凑的riemannian歧管上的梯度障碍问题家族。我们证明，这些自由边界问题的解决方案是统一的半循环，因此，我们为解决方案及其自由边界获得了一些良好的收敛结果。确切地说，我们证明了Hausdorff的解决方案的弹性和$λ$弹性集合到切割基因座和歧管的$λ$ -CUT基因座。
We study a family of gradient obstacle problems on a compact Riemannian manifold. We prove that the solutions of these free boundary problems are uniformly semiconcave and, as a consequence, we obtain some fine convergence results for the solutions and their free boundaries. Precisely, we show that the elastic and the $λ$-elastic sets of the solutions Hausdorff converge to the cut locus and the $λ$-cut locus of the manifold.
