A weakly second order differential structure on rectifiable metric measure spaces
Differential Geometry
2014-11-11 v3 Metric Geometry
Abstract
We give the definition of angles on a Gromov-Hausdorff limit space of a sequence of complete n-dimensional Riemannian manifolds with a lower Ricci curvature bound. We apply this to prove there is a weakly second order differential structure on these spaces and prove there is a unique Levi-Civita connection allowing us to define the Hessian of a twice differentiable function.
Cite
@article{arxiv.1112.0099,
title = {A weakly second order differential structure on rectifiable metric measure spaces},
author = {Shouhei Honda},
journal= {arXiv preprint arXiv:1112.0099},
year = {2014}
}
Comments
29 pages. Several statements added. The title changed