AI 中文总结
研究欧几里得和双曲背景几何中局部有限无限三角剖分上的三维组合 Yamabe 流，通过适当假设建立原始流短时存在唯一性，引入扩展流并证明其长时间存在性。
AI 中文摘要
本文研究欧几里得和双曲背景几何中局部有限无限三角剖分上的三维组合 Yamabe 流。在适当的非退化和有界度假设下，建立了原始流的短时存在性和唯一性。通过立体角的连续扩展引入扩展流，并在适当初始假设下证明了两种扩展流的长时间存在性。
英文摘要
In this paper, we study three-dimensional combinatorial Yamabe flows on locally finite infinite triangulations in Euclidean and hyperbolic background geometries. Under suitable non-degeneracy and bounded-degree assumptions, we establish the short-time existence and uniqueness of the original flows. We further introduce the extended flows by using the continuous extension of solid angles, and prove long-time existence for both extended flows under suitable initial assumptions.
Comments26 pages
