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Do I understand correctly that with sectional curvature/triangle comparison methods you can do differential geometry on non-smooth manifolds (e.g. on a cube)? I
by bmacho 1y ago
Do I understand correctly that with sectional curvature/triangle comparison methods you can do differential geometry on non-smooth manifolds (e.g. on a cube)? If so, I've completely missed this fact before.
- youcandoittoo 1y agoSure, see (2010) A curved Brunn-Minkowski inequality on the discrete hypercube, Or: What is the Ricci curvature of the discrete hypercube? http://www.yann-ollivier.org/rech/publs/cube.pdf http://www.yann-ollivier.org/rech/publs/cube.pdf Or this: (2011) A visual introduction to Riemannian curvatures and some discrete generalizations http://www.yann-ollivier.org/rech/publs/visualcurvature.pdf http://www.yann-ollivier.org/rech/publs/visualcurvature.pdf Taken from the site of Yann Ollivier http://www.yann-ollivier.org/rech/index http://www.yann-ollivier.org/rech/index