A Modica-Mortola approximation for the Steiner Problem
Antoine Lemenant, Filippo Santambrogio
TL;DR
This paper introduces a novel approximation method for the Steiner problem using elliptic energies inspired by Modica-Mortola, incorporating a weighted geodesic distance to ensure connectivity.
Contribution
It proposes a new elliptic energy-based approximation for the Steiner problem that enforces connectivity via a weighted geodesic distance term.
Findings
Provides a new approximation scheme for the Steiner problem.
Ensures connectivity through a weighted geodesic distance.
Offers potential for numerical implementation and analysis.
Abstract
In this note we present a way to approximate the Steiner problem by a family of elliptic energies of Modica-Mortola type, with an additional term relying on the weighted geodesic distance which takes care of the connexity constraint.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Mathematical Modeling in Engineering · Matrix Theory and Algorithms