3-dimensional combinatorial Yamabe flow in hyperbolic background geometry
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- by Huabin Ge and Bobo Hua PDF
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Abstract:
We study the 3-dimensional combinatorial Yamabe flow in hyperbolic background geometry. For a triangulation of a 3-manifold, we prove that if the number of tetrahedra incident to each vertex is at least 23, then there exist real or virtual ball packings with vanishing (extended) combinatorial scalar curvature, i.e., the total (extended) solid angle at each vertex is equal to $4\pi$. In this case, if such a ball packing is real, then the (extended) combinatorial Yamabe flow converges exponentially fast to that ball packing. Moreover, we prove that there is no real or virtual ball packing with vanishing (extended) combinatorial scalar curvature if the number of tetrahedra incident to each vertex is at most 22.References
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Additional Information
- Huabin Ge
- Affiliation: School of Mathematics, Renmin University of China, Beijing, 100872, People’s Republic of China
- MR Author ID: 955742
- Email: hbge@ruc.edu.cn
- Bobo Hua
- Affiliation: School of Mathematical Sciences, LMNS, Fudan University, Shanghai 200433, China; and Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, China
- MR Author ID: 865783
- Email: bobohua@fudan.edu.cn
- Received by editor(s): April 29, 2019
- Received by editor(s) in revised form: November 25, 2019
- Published electronically: April 28, 2020
- Additional Notes: The first author was supported by the NSFC of China (No. 11871094).
The second author was supported by the NSFC of China (No. 11831004 and No. 11826031). - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 5111-5140
- MSC (2010): Primary 51M10, 52C17, 05E45
- DOI: https://doi.org/10.1090/tran/8062
- MathSciNet review: 4127872