PreprintCC BY-ND 4.0HAL
Minimal surfaces: A Lagrangian derivation of first and second variations
Abstract
This article develops a rigorous Lagrangian formulation of variational calculus for minimal surfaces, using extensively the concept of pullback covariant derivative. The goal of this paper is not to present new results on this extensively studied problem, but rather to introduce geometrical arguments that simplify the calculations and eliminate the need for ad hoc assumptions throughout the analysis. In particular, first and second normal variations are derived this way. The example of the soap film between two rings is generalized to arbitrary variations (and not just axisymmetric ones).
Related
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BibTeX
@misc{lloria2026minimal,
title = {{Minimal surfaces: A Lagrangian derivation of first and second variations}},
author = {Romain Lloria and Boris Kolev},
howpublished = {HAL},
year = {2026},
month = jun,
eprint = {2606.05969},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05643505v3},
note = {CC BY-ND 4.0},
}
RIS
TY - UNPB
TI - Minimal surfaces: A Lagrangian derivation of first and second variations
AU - Romain Lloria
AU - Boris Kolev
PY - 2026
DA - 2026/06/03
PB - HAL
UR - https://hal.science/hal-05643505v3
AB - This article develops a rigorous Lagrangian formulation of variational calculus for minimal surfaces, using extensively the concept of pullback covariant derivative. The goal of this paper is not to present new results on this extensively studied problem, but rather to introduce geometrical arguments that simplify the calculations and eliminate the need for ad hoc assumptions throughout the analysis. In particular, first and second normal variations are derived this way. The example of the soap film between two rings is generalized to arbitrary variations (and not just axisymmetric ones).
ER -