发表机构
School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究无限三角剖分双曲曲面上组合Yamabe流，在特定条件下建立其光滑解短时存在性与唯一性，引入扩展流并证明其解全局存在与唯一性，为该流提供适定性理论。
AI 中文摘要
我们研究具有分段双曲度量的无限三角剖分曲面上的组合Yamabe流。在顶点度一致有界和初始度量为$\epsilon$-一致非退化的假设下，首先建立了组合Yamabe流光滑解的短时存在性。在初始度量的附加$\epsilon$-一致Delaunay条件下，进一步得到了流解的短时唯一性。为解决沿演化过程中三角形的潜在退化问题，引入了具有广义曲率的扩展流，并建立了扩展流解的全局存在性。此外，在顶点度一致有界和一些可积性条件下，建立了该扩展流解的唯一性。这些结果为无限三角剖分曲面上的双曲组合Yamabe流（局部时间）及其扩展流（全局时间）提供了适定性理论。
英文摘要
We study the combinatorial Yamabe flow on infinitely triangulated surfaces with piecewise hyperbolic metrics. Under the assumptions of uniformly bounded vertex degree and an $ε$-uniformly nondegenerate initial metric, we establish the short-time existence and uniqueness of smooth solutions to the combinatorial Yamabe flow. To address the potential degeneration of triangles along the evolution, we introduce an extended flow with generalized curvature, and establish the global existence of solutions to the extended flow.Furthermore, under an integrability condition, we establish the uniqueness of solutions to this extended flow, which follows from the stability property of the solutions. These results provide a local well-posedness theory for the hyperbolic combinatorial Yamabe flow on infinitely triangulated surfaces.
Comments23 pages, uniform Delaunay condition is removed and typos are corrected
