The space of functions of bounded variation on curves in metric measure spaces

DOI10.1090/ecgd/291zbMath1338.26006OpenAlexW2342376315MaRDI QIDQ2802140

Olli Martio

Publication date: 25 April 2016

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/ecgd/291

zbMATH Keywords

functions of bounded variationmetric measure spaceAM-modulus

Mathematics Subject Classification ID

Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Functions of bounded variation, generalizations (26A45) Analysis on metric spaces (30L99)

Related Items (6)

Plans on measures and \textit{AM}-modulus ⋮ Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality ⋮ Functions of bounded variation and the \(AM\)-modulus in \(\mathbb{R}^n\) ⋮ On master test plans for the space of BV functions ⋮ AM‐modulus and Hausdorff measure of codimension one in metric measure spaces ⋮ A version of Stokes's theorem using test curves

Cites Work

• Unnamed Item
• Unnamed Item
• Functions of bounded variation and curves in metric measure spaces
• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• On the duality between \(p\)-modulus and probability measures
• Nonlinear potential theory on metric spaces
• Semmes family of curves and a characterization of functions of bounded variation in terms of curves
• Extremal length and functional completion
• Functions of bounded variation on ``good metric spaces
• Quasiconformal maps in metric spaces with controlled geometry
• Lectures on analysis on metric spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Equivalent definitions of \(BV\) space and of total variation on metric measure spaces

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