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- W4366999426 abstract "In this paper, we investigate the relation between energy-minimizing torus-valued maps with prescribed singularities, the lifting problem for torus-valued maps in the space BV, and Plateau's problem for vectorial currents, in codimension one. First, we show that the infimum of the $W^{1,1}$-seminorm among all maps with values in the $k$-dimensional flat torus and prescribed topological singularities $S$ is equal to the minimum of the mass among all $textit{normal}$ $mathbb{R}^k$-currents, of codimension one, bounded by $S$. Then, we show that the minimum of the $BV$-energy among all liftings of a given torus-valued $W^{1,1}$-map $textbf{u}$ can be expressed in terms of the minimum mass among all $textit{integral}$ $mathbb{Z}^k$-currents, of codimension one, bounded by the singularities of $textbf{u}$. As a byproduct of our analysis, we provide a bound for the solution of the integral Plateau problem, in codimension one, in terms of Plateau's problem for normal currents." @default.
- W4366999426 created "2023-04-27" @default.
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- W4366999426 date "2023-04-22" @default.
- W4366999426 modified "2023-10-01" @default.
- W4366999426 title "Energy-minimizing torus-valued maps with prescribed singularities, Plateau's problem, and BV-lifting" @default.
- W4366999426 doi "https://doi.org/10.48550/arxiv.2304.11349" @default.
- W4366999426 hasPublicationYear "2023" @default.
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