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February 26, 2026Milan Journal of MathematicsOpen Access

Minimal Horizontal Triods: Analysis and Computation

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Authors

RNRobert NürnbergPPPaola Pozzi

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Overview

This article analyzes minimal length connections among three points in a geometric space, suggesting improved understanding of sub-Riemannian geometry.

Key Points

  • The aim is to find and characterize minimal horizontal triods connecting three points in the Heisenberg group.
  • Proved the existence of minimal horizontal triods.
  • Characterized these triods for further analysis.
  • Formulated a horizontal curve shortening flow to deform initial triods into critical points.
  • Conducted numerical experiments using a fully discrete finite element scheme.
  • Identified various forms of minimal horizontal triods.
  • Established the effectiveness of the curve shortening flow.
  • Demonstrated rich geometrical insights through numerical experiments.

Cite This Study

Nürnberg et al. (2026) studied this question.

synapsesocial.com/papers/699fe40c95ddcd3a253e8408https://doi.org/10.1007/s00032-025-00428-w
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