#### Volume 18, issue 2 (2014)

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A weakly second-order differential structure on rectifiable metric measure spaces

### Shouhei Honda

Geometry & Topology 18 (2014) 633–668
##### Abstract

We give a definition of angles on the 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 that they admit a unique Levi-Civita connection, allowing us to define the Hessian of a twice differentiable function.

##### Keywords
Gromov–Hausdorff convergence, Ricci curvature, geometric measure theory
Primary: 53C20
Secondary: 53C21