From volume cone to metric cone in the nonsmooth setting

By Guido De Philippis, Nicola Gigli. 2015

86 citations recorded by the source corpus.

We prove that ‘volume cone implies metric cone’ in the setting of $${\mathsf{RCD}}$$RCD spaces, thus generalising to this class of spaces a well known result of Cheeger–Colding valid in Ricci-limit spaces.

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

View Paper: https://www.semanticscholar.org/paper/ee3b23ec93ce97ba25cec7eed43a910684e91f95

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. Luca Tamanini
2. Nicola Gigli
3. Luigi Ambrosio
4. Andrea Mondino
5. Giuseppe Savar'e
6. Elia Brué
7. Filippo Santambrogio
8. Fabio Cavalletti

In Astronomy and Astrophysics

1. Luca Tamanini
2. Nicola Gigli
3. Luigi Ambrosio
4. Andrea Mondino
5. Giuseppe Savar'e
6. Fabio Cavalletti
7. T. Rajala
8. C. Ketterer

In Geometry and Topology

1. Luca Tamanini
2. Nicola Gigli
3. Luigi Ambrosio
4. Filippo Santambrogio
5. Giuseppe Savar'e
6. Matthias Erbar
7. C. Ketterer
8. Andrea Mondino

Citations in the corpus

• Second order differentiation formula on RCD*$(K,N)$ spaces (2018, background): “For instance, the proofs of both the splitting theorem [7] and of the ‘volume cone implies metric cone’ [5] in this setting can be greatly simplified by using such formula (in this direction, see [14] for comments about the splitting).”