Closed n-manifolds with diam² sec ≥ -κ and diam² Ric ≥ -δ (δ small depending on n,κ) fiber over a b1(M)-torus, removing the upper sectional curvature bound from Yamaguchi's prior result.
Behaviour of the reference measure on $\sf RCD$ spaces under charts
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Mondino and Naber recently proved that finite dimensional $\sf RCD$ spaces are rectifiable. Here we show that the push-forward of the reference measure under the charts built by them is absolutely continuous with respect to the Lebesgue measure. This result, read in conjunction with another recent work of us, has relevant implications on the structure of tangent spaces to $\sf RCD$ spaces. A key tool that we use is a recent paper by De Philippis-Rindler about the structure of measures on the Euclidean space.
fields
math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Fibrations, the First Betti Number, and Almost Nonnegative Ricci Curvature
Closed n-manifolds with diam² sec ≥ -κ and diam² Ric ≥ -δ (δ small depending on n,κ) fiber over a b1(M)-torus, removing the upper sectional curvature bound from Yamaguchi's prior result.