Minimal surfaces: A Lagrangian derivation of first and second variations

Romain Lloria; Boris Kolev

doi:10.48550/arxiv.2606.05969

June 4, 2026Open Access

Minimal surfaces: A Lagrangian derivation of first and second variations

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Key Points

The aim is to establish a rigorous Lagrangian formulation for variational calculus applied to minimal surfaces.
Developed a formulation using pullback covariant derivative.
Utilized geometric arguments to show that all tangential variations vanish.
Derived both first and second normal variations.
Confirmed that all tangential variations are zero.
Successfully derived first normal variations showing consistent results.
Calculated second normal variations with established geometric principles.

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Implication

This article develops a Lagrangian framework to derive variations in minimal surfaces, suggesting new insights into geometric calculus.

Abstract

This article develops a rigorous Lagrangian formulation of variational calculus for minimal surfaces, using extensively the concept of pullback covariant derivative. It is shown, in particular, using a geometric argument that all tangential variations vanish. First and second normal variations are then derived.

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Lloria et al. (2026) studied this question.

synapsesocial.com/papers/6a27ad11a963992e1626770e https://doi.org/10.48550/arxiv.2606.05969

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Minimal surfaces: A Lagrangian derivation of first and second variations

Key Points

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Implication

Abstract

Discussion

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Minimal surfaces: A Lagrangian derivation of first and second variations

Key Points

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Implication

Abstract

Discussion

Cite This Study

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