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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Combinatorial Calabi flows on surfaces
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by Huabin Ge PDF
Trans. Amer. Math. Soc. 370 (2018), 1377-1391 Request permission

Abstract:

For triangulated surfaces, we introduce the combinatorial Calabi flow which is an analogue of the smooth Calabi flow. We prove that the solution to the combinatorial Calabi flow exists for all time and converges if and only if the Thurston’s circle packing exists. As a consequence, the combinatorial Calabi flow provides a new algorithm to find circle packings with prescribed curvatures. The proofs rely on careful analysis of the combinatorial Calabi energy, combinatorial Ricci potential and discrete dual-Laplacians.
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Additional Information
  • Huabin Ge
  • Affiliation: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, People’s Republic of China
  • MR Author ID: 955742
  • Email: hbge@bjtu.edu.cn
  • Received by editor(s): March 10, 2015
  • Received by editor(s) in revised form: July 5, 2016, and December 23, 2016
  • Published electronically: October 16, 2017
  • Additional Notes: This research was supported by the National Natural Science Foundation of China under grant No.11501027, and Fundamental Research Funds for the Central Universities (Nos. 2015JBM103, 2014RC028 and 2016JBM071).
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 1377-1391
  • MSC (2010): Primary 53C44, 52C26
  • DOI: https://doi.org/10.1090/tran/7196
  • MathSciNet review: 3729504