On the structure of spaces with Ricci curvature bounded below. II
By Jeff Cheeger, T. Colding. 2000
1,033 citations recorded by the source corpus.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/523f8bdd505c039d7792aa0c4dfb1e73e023da49
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
- Nicola Gigli
- Andrea Mondino
- G'abor Sz'ekelyhidi
- Luigi Ambrosio
- Fabio Cavalletti
- G. Tian
- J. Lott
- Chi Li
In Astronomy and Astrophysics
- Nicola Gigli
- Andrea Mondino
- Fabio Cavalletti
- Luigi Ambrosio
- T. Rajala
- Elia Brué
- G'abor Sz'ekelyhidi
- Daniele Semola
In Geometry and Topology
Citations in the corpus
- Smooth Convergence Away from Singular Sets (2012, methodology): “Thus, we can apply the noncollapsing theory of Cheeger–Colding [5] to see that after possibly taking another subsequence of (M, gi) we can control the volumes of the limit space’s balls: For all y ∈ Y , there exists yi ∈M such that”
- Monotonicity and its analytic and geometric implications (2012, neutral): “QðrÞ ≤ C ðlog rÞ1þε : [23]”
- On the differential structure of metric measure spaces and applications (2012, background): “The proof we propose has the advantage of being simple and of avoiding the use of the almost splitting theorem, although clearly to (hope to) recover the results in [14], [15], [16] in the non-smooth context a lot of work has still to be done.”
- Weak curvature conditions and functional inequalities (2005, methodology): “The method of proof was to show that such Riemannian manifolds satisfy a certain “segment inequality” [3, Theorem 2.11] and then to show that the property of satisfying the segment inequality is preserved under measured Gromov–Hausdorff limits [ 4, Theorem 2.6 ].”
- Geometric estimates for complex Monge–Ampère equations (2017, methodology): “We define a function onX Œ0;1/ as the normalized volume ([5]) V k.”
- Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds (2022, background): “This is the so-called volume convergence theorem, originally proved in [38, 35] for smooth manifolds and their limits and extended in [42] to the present setting.”