Analytic Deformations of Minimal Networks

TL;DR

This paper investigates how minimal networks such as spanning trees and shortest trees behave under boundary deformations, showing that analyticity of the deformation preserves their types in Euclidean space.

Contribution

It demonstrates that analyticity of boundary deformations guarantees the preservation of minimal network types, extending understanding of network stability under boundary changes.

Findings

Analytic boundary deformations preserve network types.

Minimal spanning trees and fillings remain stable under such deformations.

The results apply specifically to Euclidean space.

Abstract

A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal fillings and so-called stable shortest trees in the Euclidean space.