English

On exterior calculus and curvature in piecewise-flat manifolds

Differential Geometry 2012-12-06 v1 General Relativity and Quantum Cosmology

Abstract

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.

Keywords

Cite

@article{arxiv.1212.0919,
  title  = {On exterior calculus and curvature in piecewise-flat manifolds},
  author = {Jonathan R. McDonald and Warner A. Miller and Paul M. Alsing and Xianfeng D. Gu and Xuping Wang and Shing-Tung Yau},
  journal= {arXiv preprint arXiv:1212.0919},
  year   = {2012}
}

Comments

27 pages, 5 figures