Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below

By Nicola Gigli, Andrea Mondino, T. Rajala. 2013

65 citations recorded by the source corpus.

We show that in any infinitesimally Hilbertian CD � (K,N)-space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space that converges to a Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof follows by considering iterated tangents and the splitting theorem for infinitesimally Hilbertian CD � (0,N)-spaces.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/00e724708bf8c7d4eeb1d8e65d503965607da4ca

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Enrico Pasqualetto
2. Elia Brué
3. Semola Daniele
4. Yu Kitabeppu
5. Sajjad Lakzian

In Astronomy and Astrophysics

1. Enrico Pasqualetto
2. Elia Brué
3. Yu Kitabeppu
4. Semola Daniele
5. Sajjad Lakzian

In Geometry and Topology

1. Semola Daniele
2. Elia Brué
3. Enrico Pasqualetto
4. Yu Kitabeppu
5. Sajjad Lakzian

Citations in the corpus

• Rectifiability of the reduced boundary for sets of finite perimeter over $\RCD(K,N)$ spaces. (2019, background): “3 the state of the art in the theory of sets of finite perimeter was similar to that of the structure theory of RCD spaces after [31], where the authors proved existence of a Euclidean tangent space up to negligible sets.”
• Characterization of Low Dimensional RCD*(K, N) Spaces (2015, methodology): “From the work of Gigli-Mondino-Rajala [23] and Mondino-Naber [32], it follows that: Theorem 2.”