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Qualitative Properties of Maximum Distance Minimizers and Average Distance Minimizers in Rn

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Abstract

We consider one-dimensional networks of finite length in \(\mathbb{R}^n \) 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 S1), and have some mild regularity properties.Bibliography: 11 titles.

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Authors
  1. E. Paolini
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  2. E. Stepanov
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Paolini, E., Stepanov, E. Qualitative Properties of Maximum Distance Minimizers and Average Distance Minimizers in Rn . Journal of Mathematical Sciences 122, 3290–3309 (2004). https://doi.org/10.1023/B:JOTH.0000031022.10122.f5

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  • DOI: https://doi.org/10.1023/B:JOTH.0000031022.10122.f5

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