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On exterior calculus and curvature in piecewise-flat manifolds

Jonathan R McDonald Warner A Miller Paul M Alsing Xianfeng D Gu Xuping Wang Shing-Tung Yau

Differential Geometry mathscidoc:1912.43639

arXiv preprint arXiv:1212.0919, 2012.12
Simplicial, piecewise-flat discretizations of manifolds provide a clear path towards curvature analysis on discrete geometries and for solutions of PDE's on manifolds of complex topologies. In this manuscript we review and expand on discrete exterior calculus methods using hybrid domains. We then analyze the geometric structure of curvature operators in a piecewise-flat lattice.
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@inproceedings{jonathan2012on,
  title={On exterior calculus and curvature in piecewise-flat manifolds},
  author={Jonathan R McDonald, Warner A Miller, Paul M Alsing, Xianfeng D Gu, Xuping Wang, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204635151473203},
  booktitle={arXiv preprint arXiv:1212.0919},
  year={2012},
}
Jonathan R McDonald, Warner A Miller, Paul M Alsing, Xianfeng D Gu, Xuping Wang, and Shing-Tung Yau. On exterior calculus and curvature in piecewise-flat manifolds. 2012. In arXiv preprint arXiv:1212.0919. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204635151473203.
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