@inproceedings{0e0d8d5e98b247449c13a8c8a563caec,
title = "Discrete curvature flows for surfaces and 3-manifolds",
abstract = "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.",
keywords = "3-manifold, Curvature flow, Discrete, Surface, The ricci flow, Yamabe flow",
author = "Xiaotian Yin and Miao Jin and Feng Luo and Gul, \{Xianfeng David\}",
year = "2009",
doi = "10.1007/978-3-642-00826-9\_3",
language = "English",
isbn = "9783642008252",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "38--74",
booktitle = "Emerging Trends in Visual Computing - LIX Fall Colloquium, ETVC 2008, Revised Invited Papers",
note = "LIX Fall Colloquium on Emerging Trends in Visual Computing, ETVC 2008 ; Conference date: 18-11-2008 Through 20-11-2009",
}