On the structure of flat chains modulo p
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Andrea Marchese
Abstract
In this paper, we prove that every equivalence class in the quotient group of integral 1-currents modulo p in Euclidean space contains an integral current, with quantitative estimates on its mass and the mass of its boundary. Moreover, we show that the validity of this statement for m-dimensional integral currents modulo p implies that the family of
Funding source: FP7 Ideas: European Research Council
Award Identifier / Grant number: 306246
Funding statement: Both authors are supported by the ERC-grant RAM “Regularity of Area Minimizing currents”, ID 306246.
Acknowledgements
The authors would like to thank Camillo De Lellis for having posed the problem and for helpful discussions. We are also grateful to the anonymous referee for his/her valuable comments.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Local regularity and compactness for the p-harmonic map heat flows
- 𝒟1,2(ℝN) versus C(ℝN) local minimizer on manifolds and multiple solutions for zero-mass equations in ℝN
- Existence and regularity results for weak solutions to (p,q)-elliptic systems in divergence form
- On a new class of fractional partial differential equations II
- On the structure of flat chains modulo p
- A remark on the two-phase obstacle-type problem for the p-Laplacian
Artikel in diesem Heft
- Frontmatter
- Local regularity and compactness for the p-harmonic map heat flows
- 𝒟1,2(ℝN) versus C(ℝN) local minimizer on manifolds and multiple solutions for zero-mass equations in ℝN
- Existence and regularity results for weak solutions to (p,q)-elliptic systems in divergence form
- On a new class of fractional partial differential equations II
- On the structure of flat chains modulo p
- A remark on the two-phase obstacle-type problem for the p-Laplacian
