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Maps of bounded variation from PI spaces to metric spaces

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arxiv 2306.00768 v2 pith:QQLEMCMM submitted 2023-06-01 math.FA math.APmath.MG

Camillo Brena , Francesco Nobili , Enrico Pasqualetto This is my paper · ORCID
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keywords mapsmetricspaceboundedspacesvariationapproximationassuming
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We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincar\'e property, we produce a well-behaved relaxation theory via approximation by simple maps. Moreover, several equivalent characterizations are given, including a notion in weak duality with test plans.

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Cited by 3 Pith papers

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

  1. 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.

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    math.MG 2024-12 conditional novelty 6.0 of 10

    Any gap-free packing of a bag by countably many positive-volume sets that touch on zero-area sets must have infinite total surface area.

  3. 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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