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Mathematics > Metric Geometry

arXiv:2207.12191 (math)
[Submitted on 25 Jul 2022 (v1), last revised 24 Sep 2024 (this version, v6)]

Title:Korevaar-Schoen-Sobolev spaces and critical exponents in metric measure spaces

Authors:Fabrice Baudoin
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Abstract:We present developments in the theory of Korevaar-Schoen-Sobolev spaces on metric measure spaces. While this theory coincides with those of Cheeger and Shanmugalingam if the space is doubling and satisfies a Poincaré inequality, it offers new perspectives in the context of fractals for which the approach by weak upper gradients is inadequate.
Comments: Previous version of the manuscript was used as Lecture Notes for the mini course hold at Texas A&M during the workshop Geometry and Analysis on Nonsmooth Spaces, August 8-12 2022. v6: Final version to appear in Ann. Fenn
Subjects: Metric Geometry (math.MG); Functional Analysis (math.FA)
Cite as: arXiv:2207.12191 [math.MG]
  (or arXiv:2207.12191v6 [math.MG] for this version)
  https://doi.org/10.48550/arXiv.2207.12191

Submission history

From: Fabrice Baudoin Dr [view email]
[v1] Mon, 25 Jul 2022 13:30:22 UTC (713 KB)
[v2] Sun, 7 Aug 2022 01:37:59 UTC (718 KB)
[v3] Sun, 21 Aug 2022 15:03:32 UTC (720 KB)
[v4] Fri, 28 Apr 2023 12:44:11 UTC (720 KB)
[v5] Wed, 13 Mar 2024 17:58:12 UTC (721 KB)
[v6] Tue, 24 Sep 2024 13:44:16 UTC (721 KB)
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