论文标题
紧凑型紫红色歧管具有凸边界的刚度
Rigidity of compact Fuchsian manifolds with convex boundary
论文作者
论文摘要
带边界的紧凑型紫红色歧管是一个双曲线3型同型同构至$ s_g \ times [0; 1] $使得边界组件$ s_g \ times \ {0 \} $是Geodesic。我们证明，带有凸边界的紧凑型紫红色歧管由$ s_g \ times \ {1 \} $上的感应路径度量唯一确定。除了凸度以外，我们没有对边界提出进一步的限制。
A compact Fuchsian manifold with boundary is a hyperbolic 3-manifold homeomorphic to $S_g \times [0; 1]$ such that the boundary component $S_g \times \{ 0\}$ is geodesic. We prove that a compact Fuchsian manifold with convex boundary is uniquely determined by the induced path metric on $S_g \times \{1\}$. We do not put further restrictions on the boundary except convexity.
