We extend to the higher dimension results about minimal connections and optimal lifting of maps of bounded variation with values into S^1. Namely, we first outline the link between lifting and connections of maps in BV(B^n,S^1). We then write in an explicit way the energy of the optimal lifting of BV-maps. Finally, we show that the minimal connection can be seen as the distance from gradient maps.
BV-maps with values into S^1: graphs, minimal connections and optimal lifting / Mucci, Domenico. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 20:5(2008), pp. 859-880. [10.1515/FORUM.2008.041]
BV-maps with values into S^1: graphs, minimal connections and optimal lifting
MUCCI, Domenico
2008
Abstract
We extend to the higher dimension results about minimal connections and optimal lifting of maps of bounded variation with values into S^1. Namely, we first outline the link between lifting and connections of maps in BV(B^n,S^1). We then write in an explicit way the energy of the optimal lifting of BV-maps. Finally, we show that the minimal connection can be seen as the distance from gradient maps.
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