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

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
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
##### Publication
Received: 5 March 2013
Accepted: 28 September 2013
Published: 20 March 2014
Proposed: Dmitri Burago
Seconded: John Lott, Tobias H Colding
##### Authors
 Shouhei Honda Faculty of Mathmatics Kyushu University 744, Motooka Nishi-Ku Fukuoka 819-0395 Japan