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arXiv · 1112.0099

A weakly second order differential structure on rectifiable metric measure spaces

Shouhei Honda
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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.

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Shouhei Honda. 2013-03-05. A weakly second order differential structure on rectifiable metric measure spaces. https://doi.org/10.2140/gt.2014.18.633

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