On the equality between the infima obtained by solving various Plateau's problems
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Publication:6103496
DOI10.1016/j.aim.2023.109106arXiv1910.00231OpenAlexW4378699255MaRDI QIDQ6103496
Chun Yan Liu, Yangqin Fang, Vincent Feuvrier
Publication date: 5 June 2023
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1910.00231
Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Other homology theories in algebraic topology (55N35)
Cites Work
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- Allard-type boundary regularity for \(C^{1,\alpha}\) boundaries
- Comparison of singular and Čech homology in locally connected spaces
- Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
- Comparing homologies: Čech's theory, singular chains, integral flat chains and integral currents
- Hölder regularity of two-dimensional almost-minimal sets in \(\mathbb R^n\)
- Size-minimizing rectifiable currents
- On the first variation of a varifold: Boundary behavior
- The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
- The deformation theorem for flat chains
- Existence of solutions to a general geometric elliptic variational problem
- Rectifiability of flat chains
- Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure
- Normal and integral currents
- A proof of the regularity everywhere of the classical solution to Plateau's problem
- On axiomatic homology theory
- Existence of minimizers for the Reifenberg Plateau problem
- Remplissage De L'Espace Euclidien Par Des Complexes Poly\'Edriques D'Orientation Impos\'Ee Et De Rotondit\'E Uniforme
- Should we solve Plateau's problem again?
- Size minimizing surfaces
- SIMPLICIAL VOLUMES OF ALEXANDROV SPACES
- Flat Chains Over a Finite Coefficient Group
- Axiomatic Approach to Homology Theory
- Local 𝐶^{1,𝛽}-regularity at the boundary of two dimensional sliding almost minimal sets in ℝ³
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