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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 · ORCID
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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Forward citations

Cited by 9 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

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    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.

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    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.

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    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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    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. Barycenter curvature-dimension condition for extended metric measure spaces

    math.MG 2025-01 conditional novelty 4.0 of 10

    A new barycenter-based curvature-dimension condition, BCD(K,∞), is defined and shown to follow from EVI gradient-flow theory on RCD, Wiener, and configuration spaces.

  7. 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.

  8. An overview of regularity results for the Laplacian and $p$-Laplacian in metric spaces

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    A survey of regularity estimates for the Laplacian and p-Laplacian on metric measure spaces, with a proof overview of the author's second-order regularity theorem in bounded RCD spaces.

  9. An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds

    math.AP 2024-12 accept novelty 2.0 of 10

    The paper reviews and re-exposes existing stability theorems for sharp Sobolev inequalities on manifolds with Ricci lower bounds.

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