论文标题
通过Arnaud的定理的奇异函数集的拓扑
Topology of singular set of semiconcave function via Arnaud's theorem
论文作者
论文摘要
我们证明了具有线性模量通常的单数半循环函数的某些子集的某些子集的（局部）路径连接性。从某种意义上说，这个结果是最佳的。证明基于Marie-Claude Arnaud的定理（M.-C。Arnaud，\ textit {pseudographs和Lax-oleinik sem-Group：几何和动态解释}。我们还为时间依赖性案例提供了定理的新证明。
We proved the (local) path-connectedness of certain subset of the singular set of semiconcave functions with linear modulus in general. In some sense this result is optimal. The proof is based on a theorem by Marie-Claude Arnaud (M.-C. Arnaud, \textit{Pseudographs and the Lax-Oleinik semi-group: a geometric and dynamical interpretation}. Nonlinearity, \textbf{24}(1): 71-78, 2011.). We also gave a new proof of the theorem in time-dependent case.
