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De Giorgi and Gromov working together

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arxiv 2306.14604 v1 pith:VNXBQXRK submitted 2023-06-26 math.MG

Nicola Gigli This is my paper
classification math.MG
keywords convergencegiorgigromovtogetheractuallyalthoughconceptsfruitfully
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Mean curvature and sharp Willmore inequalities in metric spaces

    math.DG 2026-07 accept novelty 7.5 of 10

    Level sets of electrostatic potentials on RCD(0,N) spaces carry an L2 mean curvature vector satisfying the classical sharp Willmore inequality with rigidity and almost-rigidity.

  2. Stability of local Riemannian Ricci curvature lower bounds

    math.DG 2026-07 accept novelty 7.0 of 10

    Local RCD(K(·),N(·)) bounds are stable under pointed measured Gromov convergence, via a local EVI with remainder and Lagrangian Mosco convergence of Cheeger energies.

  3. Quantitative stability in distribution for the Sobolev inequality under curvature dimension condition

    math.AP 2026-07 accept novelty 7.0 of 10

    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.

  4. Warped products over one-dimensional base spaces and the RCD condition

    math.DG 2025-06 conditional novelty 7.0 of 10

    An N-warped product over a one-dimensional base satisfies the RCD(KN,N+1) curvature condition exactly when the warping function is K-concave, obeys a boundary condition, and the fiber satisfies a related RCD condition.

  5. Mosco-convergence of Cheeger energies on varying spaces satisfying curvature dimension conditions

    math.MG 2025-11 conditional novelty 6.0 of 10

    Cheeger p-energies and BV total variations are lower-semicontinuous along pointed-measure Gromov–Hausdorff limits of essentially non-branching CD(K,N) and MCP(K,N) spaces, with a 2^N factor in the MCP case.

  6. Isoperimetric problems and lower bounds on curvature

    math.DG 2025-09 conditional novelty 2.0 of 10

    Survey of isoperimetric problems under lower Ricci curvature bounds, presenting sharp concavity inequalities, recent existence results, and open questions.

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