We consider one-dimensional networks of finite length in Rn minimizing the average distance functional and the maximum distance functional subject to the length constraint. Under natural conditions, such minimizers use maximum available length, cannot contain closed loops (i.e., homeomorphic images of a circumference S_1), and have some mild regularity properties.
Qualitative properties of maximum distance minimizers and average distance minimizers in Rn
PAOLINI, EMANUELE;
2004-01-01
Abstract
We consider one-dimensional networks of finite length in Rn minimizing the average distance functional and the maximum distance functional subject to the length constraint. Under natural conditions, such minimizers use maximum available length, cannot contain closed loops (i.e., homeomorphic images of a circumference S_1), and have some mild regularity properties.File in questo prodotto:
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