Almost splitting maps, transformation theorems and smooth fibration theorems

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Methods of local Riemannian geometry (53B21)

Cites Work

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Topology and \(\epsilon\)-regularity theorems on collapsed manifolds with Ricci curvature bounds
Characterization of tangent cones of noncollapsed limits with lower Ricci bounds and applications
On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
Ricci curvature on Alexandrov spaces and rigidity theorems
Quantitative estimates on the singular sets of Alexandrov spaces
Regularity of Einstein manifolds and the codimension 4 conjecture
Collapsing Riemannian manifolds to ones of lower dimensions
Linear growth harmonic functions on a complete manifold
Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
Collapsing and pinching under a lower curvature bound
The fundamental groups of almost nonnegatively curved manifolds
Hausdorff perturbations of Ricci-flat manifolds and the splitting theorem
\(C^ \alpha\)-compactness for manifolds with Ricci curvature and injectivity radius bounded below
Ricci curvature and Betti numbers
Differentiability of Lipschitz functions on metric measure spaces
On the structure of spaces with Ricci curvature bounded below. I
Lectures on analysis on metric spaces
Local spectral convergence in \(\mathrm{RCD}^\ast(K, N)\) spaces
Recognizing the flat torus among \(\mathsf{RCD}^*(0,N)\) spaces via the study of the first cohomology group
Characterizations of monotonicity of vector fields on metric measure spaces
Large time behavior of the heat equation on complete manifolds with non- negative Ricci curvature
Linear growth harmonic functions on complete manifolds with nonnegative Ricci curvature
Smoothing Riemannian metrics with Ricci curvature bounds
Lower bounds on Ricci curvature and the almost rigidity of warped products
On the topology and the boundary of \(N\)-dimensional \(\mathsf{RCD}\,(K,N)\) spaces
Weakly non-collapsed RCD spaces are strongly non-collapsed
Ricci flow smoothing for locally collapsing manifolds
Boundary regularity and stability for spaces with Ricci bounded below
Fibrations and stability for compact group actions on manifolds with local bounded Ricci covering geometry
Weyl's law on \(RCD^{\ast} (K, N)\) metric measure spaces
A sufficient condition to a regular set being of positive measure on spaces
Structure theory of metric measure spaces with lower Ricci curvature bounds
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
Cheeger-harmonic functions in metric measure spaces revisited
Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below
Rectifiability of the reduced boundary for sets of finite perimeter over \(\operatorname{RCD} ( K , N )\) spaces
Alexandrov meets Lott--Villani--Sturm
On the differential structure of metric measure spaces and applications
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
An existence theorem of harmonic functions with polynomial growth
Non-collapsed spaces with Ricci curvature bounded from below
Local estimate on convexity radius and decay of injectivity radius in a Riemannian manifold
Manifolds of Ricci curvature and local rewinding volume bounded below
New stability results for sequences of metric measure spaces with uniform Ricci bounds from below
Collapsed manifolds with Ricci bounded covering geometry
Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure
Optimal Transport
Almost flat manifolds
A note on the topological stability theorem from RCD spaces to Riemannian manifolds
Canonical diffeomorphisms of manifolds near spheres
A finite topological type theorem for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume

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