A note on indecomposable sets of finite perimeter
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Panu Lahti
Abstract
Bonicatto, Pasqualetto and Rajala (2020) proved that a decomposition theorem for sets of finite perimeter into indecomposable sets, known to hold in Euclidean spaces, holds also in complete metric spaces equipped with a doubling measure, supporting a Poincaré inequality, and satisfying an isotropicity condition. We show that the last assumption can be removed.
Acknowledgements
The author wishes to thank Tapio Rajala for discussions and for checking the manuscript, as well as two anonymous referees for providing helpful feedback.
References
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A strict inequality for the minimization of the Willmore functional under isoperimetric constraint
- Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian
- A note on indecomposable sets of finite perimeter
- Gamma-convergence of Gaussian fractional perimeter
- A speed preserving Hilbert gradient flow for generalized integral Menger curvature
- A new proof of compactness in G(S)BD
- Interpolation inequalities for partial regularity
- Area formula for regular submanifolds of low codimension in Heisenberg groups
- Area-minimizing properties of Pansu spheres in the sub-Riemannian 3-sphere
- Gradient estimates for an orthotropic nonlinear diffusion equation
- Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition
- Integral representation of local functionals depending on vector fields
Artikel in diesem Heft
- Frontmatter
- A strict inequality for the minimization of the Willmore functional under isoperimetric constraint
- Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian
- A note on indecomposable sets of finite perimeter
- Gamma-convergence of Gaussian fractional perimeter
- A speed preserving Hilbert gradient flow for generalized integral Menger curvature
- A new proof of compactness in G(S)BD
- Interpolation inequalities for partial regularity
- Area formula for regular submanifolds of low codimension in Heisenberg groups
- Area-minimizing properties of Pansu spheres in the sub-Riemannian 3-sphere
- Gradient estimates for an orthotropic nonlinear diffusion equation
- Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition
- Integral representation of local functionals depending on vector fields
