Discrete curvature flows for surfaces and 3-manifolds

Xiaotian Yin Miao Jin Feng Luo Xianfeng David Gu

Numerical Analysis and Scientific Computing mathscidoc:1912.43803

38-74, 2008.11
Intrinsic curvature flows can be used to design Riemannian metrics by prescribed curvatures. This chapter presents three discrete curvature flow methods that are recently introduced into the engineering fields: the discrete Ricci flow and discrete Yamabe flow for surfaces with various topology, and the discrete curvature flow for hyperbolic 3-manifolds with boundaries. For each flow, we introduce its theories in both the smooth setting and the discrete setting, plus the numerical algorithms to compute it. We also provide a brief survey on their history and their link to some of the engineering applications in computer graphics, computer vision, medical imaging, computer aided design and others.
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@inproceedings{xiaotian2008discrete,
  title={Discrete curvature flows for surfaces and 3-manifolds},
  author={Xiaotian Yin, Miao Jin, Feng Luo, and Xianfeng David Gu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205910498255367},
  pages={38-74},
  year={2008},
}
Xiaotian Yin, Miao Jin, Feng Luo, and Xianfeng David Gu. Discrete curvature flows for surfaces and 3-manifolds. 2008. pp.38-74. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205910498255367.
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