Abstract
Certain Sobolev spaces of S 1-valued functions can be written as a disjoint union of homotopy classes. The problem of finding the distance between different homotopy classes in such spaces is considered. In particular, several types of one-dimensional and two-dimensional domains are studied. Lower bounds are derived for these distances. Furthermore, in many cases it is shown that the lower bounds are sharp but are not achieved.
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The first author’s work of was supported in part by NSF grant 0503887.
The second author’s research of was supported by G.S. Elkin research fund.
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Rubinstein, J., Shafrir, I. The distance between homotopy classes of S 1-valued maps in multiply connected domains. Isr. J. Math. 160, 41–59 (2007). https://doi.org/10.1007/s11856-007-0055-1
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DOI: https://doi.org/10.1007/s11856-007-0055-1