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

Honda, Shouhei¹

¹ Faculty of Mathmatics, Kyushu University, 744, Motooka, Nishi-Ku, Fukuoka 819-0395, Japan

Geometry & topology, Tome 18 (2014) no. 2, pp. 633-668.

Résumé

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.

Détail

DOI : 10.2140/gt.2014.18.633

Classification : 53C20, 53C21
Keywords: Gromov–Hausdorff convergence, Ricci curvature, geometric measure theory

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