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arXiv · 2509.01179

Structural Equations for Critical Points of Conformally Invariant Curvature Energies in 4d

Yann Bernard
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Abstract

This paper considers the Euler-Lagrange equations satisfied by the critical points of a large class of conformally invariant extrinsic energies for 4-manifolds immersed into Euclidean space (any codimension). Using invariances and Noether's theorem, we convert the Euler-Lagrange equation in a system of equations with analytically favourable structures. The present paper generalises to the four-dimensional setting ideas originally developed by Tristan Rivi\`ere in his study of the Willmore energy in two dimensions.

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Yann Bernard. 2025-09-01. Structural Equations for Critical Points of Conformally Invariant Curvature Energies in 4d. https://arxiv.org/abs/2509.01179

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