On the distance between homotopy classes in W 1/p,p (𝕊 1 ;𝕊 1 )
Confluentes Mathematici, Tome 10 (2018) no. 1, pp. 125-136.

For every p(1,) there is a natural notion of topological degree for maps in W 1/p,p (𝕊 1 ;𝕊 1 ) which allows us to write that space as a disjoint union of classes,

W1/p,p(𝕊1;𝕊1)=dd.

For every pair d 1 ,d 2 , we show that the distance

DistW1/p,p(d1,d2):=supfd1infgd2dW1/p,p(f,g)

equals the minimal W 1/p,p -energy in d 1 -d 2 . In the special case p=2 we deduce from the latter formula an explicit value: Dist W 1/2,2 ( d 1 , d 2 )=2π|d 2 -d 1 | 1/2 .

Reçu le : 2017-09-07
Révisé le : 2017-12-25
Accepté le : 2017-12-28
Publié le : 2018-09-10
DOI : https://doi.org/10.5802/cml.48
Classification : 46E35
Mots clés: 𝕊 1 -valued maps, Fractional Sobolev spaces
@article{CML_2018__10_1_125_0,
     author = {Itai Shafrir},
     title = {On the distance between homotopy classes in $W^{1/p,p}({\protect \mathbb{S}}^1;{\protect \mathbb{S}}^1)$},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {10},
     number = {1},
     year = {2018},
     pages = {125-136},
     doi = {10.5802/cml.48},
     language = {en},
     url = {cml.centre-mersenne.org/item/CML_2018__10_1_125_0/}
}
Shafrir, Itai. On the distance between homotopy classes in $W^{1/p,p}({\protect \mathbb{S}}^1;{\protect \mathbb{S}}^1)$. Confluentes Mathematici, Tome 10 (2018) no. 1, pp. 125-136. doi : 10.5802/cml.48. https://cml.centre-mersenne.org/item/CML_2018__10_1_125_0/

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