TY - JOUR
T1 - On the Deformation of Thurston’s Circle Packings with Obtuse Intersection Angles
AU - Zhang, Xiaoxiao
AU - Zheng, Tao
N1 - Publisher Copyright:
© Mathematica Josephina, Inc. 2024.
PY - 2024/9
Y1 - 2024/9
N2 - We study Thurston’s circle packings with obtuse intersection angles on closed surfaces. By using combinatorial Ricci/Calabi flows and variational principle, we extend Thurston’s existence theorem for circle packings with non-obtuse intersection angles to those with obtuse intersection angles. As consequences, we generalize the existence and convergence results related to Chow-Luo’s combinatorial Ricci flows (J Differ Geom 63(1):97–129, 2018) and Ge’s combinatorial Calabi flows (Combinatorial Methods and Geometric Equations, Thesis (Ph.D.), Peking University, Beijing, 2012, Trans Am math Soc 370(2):1377–1391, 2018, Adv Math 333:528–533, 2018).
AB - We study Thurston’s circle packings with obtuse intersection angles on closed surfaces. By using combinatorial Ricci/Calabi flows and variational principle, we extend Thurston’s existence theorem for circle packings with non-obtuse intersection angles to those with obtuse intersection angles. As consequences, we generalize the existence and convergence results related to Chow-Luo’s combinatorial Ricci flows (J Differ Geom 63(1):97–129, 2018) and Ge’s combinatorial Calabi flows (Combinatorial Methods and Geometric Equations, Thesis (Ph.D.), Peking University, Beijing, 2012, Trans Am math Soc 370(2):1377–1391, 2018, Adv Math 333:528–533, 2018).
KW - 52C26
KW - 53C44
KW - Circle packings
KW - Combinatorial Ricci potential
KW - Combinatorial Ricci/Calabi flow
UR - http://www.scopus.com/inward/record.url?scp=85196061827&partnerID=8YFLogxK
U2 - 10.1007/s12220-024-01719-1
DO - 10.1007/s12220-024-01719-1
M3 - Article
AN - SCOPUS:85196061827
SN - 1050-6926
VL - 34
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 9
M1 - 264
ER -