In CD(N-1,N) spaces with near-sharp Sobolev constant, the pushforward measure of any almost-extremal is close in Wasserstein distance to an Aubin-Talenti bubble distribution, with sharp √ε rate.
De Giorgi and Gromov working together
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The title is meant as way to honor two great mathematicians that, although never actually worked together, introduced concepts of convergence that perfectly match each other and very fruitfully interact: De Giorgi's $\Gamma$-convergence of lower semicontinuous functions and Gromov's convergence of geometric structures.
years
2026 2representative citing papers
Collapsed metric measure spaces with lower Ricci bounds and essential dimension two are topological surfaces possibly with boundary.
citing papers explorer
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Quantitative stability in distribution for the Sobolev inequality under curvature dimension condition
In CD(N-1,N) spaces with near-sharp Sobolev constant, the pushforward measure of any almost-extremal is close in Wasserstein distance to an Aubin-Talenti bubble distribution, with sharp √ε rate.
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Topology of two-dimensional collapsed spaces with lower Ricci bounds
Collapsed metric measure spaces with lower Ricci bounds and essential dimension two are topological surfaces possibly with boundary.