Consider the class of closed connected sets ⊂ R n satisfying length constraint H 1 () ≤ l with given l > 0. The paper is concerned with the properties of minimizers of the uniform distance F M of to a given compact set M ⊂ R n , F M () := max dist (y, ), y∈M where dist (y, ) stands for the distance between y and . The paper deals with the planar case n = 2. In this case it is proven that the minimizers (apart trivial cases) cannot contain closed loops. Further, some mild regularity properties as well as structure of minimizers is studied.
On one-dimensional continua uniformly approximating planar sets
PAOLINI, EMANUELE;
2006-01-01
Abstract
Consider the class of closed connected sets ⊂ R n satisfying length constraint H 1 () ≤ l with given l > 0. The paper is concerned with the properties of minimizers of the uniform distance F M of to a given compact set M ⊂ R n , F M () := max dist (y, ), y∈M where dist (y, ) stands for the distance between y and . The paper deals with the planar case n = 2. In this case it is proven that the minimizers (apart trivial cases) cannot contain closed loops. Further, some mild regularity properties as well as structure of minimizers is studied.File in questo prodotto:
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