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This article is cited in 1 scientific paper (total in 1 paper)
A Note on the Weighted Yamabe Flow
Theodore Yu. Popelensky Moscow Center for Fundamental and Applied Mathematics,
Moscow State University,
Leninskie Gory 1, 119991 Moscow, Russia
Abstract:
For two dimensional surfaces (smooth) Ricci and Yamabe flows are equivalent. In
2003, Chow and Luo developed the theory of combinatorial Ricci flow for circle packing metrics
on closed triangulated surfaces. In 2004, Luo developed a theory of discrete Yamabe flow for
closed triangulated surfaces. He investigated the formation of singularities and convergence to
a metric of constant curvature.
In this note we develop the theory of a naïve discrete Ricci flow and its modification — the
so-called weighted Ricci flow. We prove that this flow has a rich family of first integrals and
is equivalent to a certain modification of Luo’s discrete Yamabe flow. We investigate the types
of singularities of solutions for these flows and discuss convergence to a metric of weighted
constant curvature.
Keywords:
combinatorial Yamabe flow, combinatorial Ricci flow, weighted flow.
Received: 27.09.2022 Accepted: 17.04.2023
Citation:
Theodore Yu. Popelensky, “A Note on the Weighted Yamabe Flow”, Regul. Chaotic Dyn., 28:3 (2023), 309–320
Linking options:
https://www.mathnet.ru/eng/rcd1207 https://www.mathnet.ru/eng/rcd/v28/i3/p309
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Abstract page: | 77 | References: | 18 |
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