几何超理想三角剖分的局部组合判据：基于组合Ricci流
Local Combinatorial Criteria for Geometric Hyper-ideal Triangulations via Combinatorial Ricci Flow
- Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study（东京大学宇宙物理数学研究所（WPI））
- Graduate School of Mathematical Sciences, The University of Tokyo（东京大学大学院数理科学研究科）
- RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所跨学科理论与数学科学中心（iTHEMS））
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过组合Ricci流为双曲截断四面体实现理想三角剖分提供局部组合判据，涵盖度为7和6的边条件，证明零曲率超理想度量的唯一性与指数收敛。
AI中文摘要：
我们给出了由非退化双曲截断四面体实现给定理想三角剖分的局部组合判据。一个局部双色判据允许度为7的边，当与低度边相接的四面体至多使用两类商边时成立。利用扩展的组合Ricci流，我们获得了最小度为6的三角剖分的参数依赖判据。对称和成对最小角估计给出了显式的度条件，包括对整个边星的混合条件。证明使用了解析角不等式和严格的区间求值。显式的面配对实现了这些判据并区分了其适用范围，而循环构造和有限覆盖则给出了无限族。每个判据都产生唯一的零曲率超理想度量，并且从任何正初始长度向量出发都具有指数收敛性。
英文摘要：
We give local combinatorial criteria for realizing prescribed ideal triangulations by nondegenerate hyperbolic truncated tetrahedra. A local bichromatic criterion allows valence-7 edges when tetrahedra meeting low-valence edges use at most two quotient-edge classes. Using the extended combinatorial Ricci flow, we obtain parameter-dependent criteria for triangulations of minimum valence 6. Symmetric and pair-min angle estimates yield explicit valence conditions, including mixed conditions on entire edge stars. The proofs use analytic angle inequalities and rigorous interval evaluations. Explicit face pairings realize the criteria and distinguish their scope, while cyclic constructions and finite covers give infinite families. Each criterion yields a unique zero-curvature hyper-ideal metric and exponential convergence from any positive initial length vector.
