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arXiv · 2606.24682

The linearized minimal surfaces problem

Haim Grebnev·Plamen Stefanov·Gunther Uhlmann·Hanming Zhou
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Abstract

We characterize the kernel of the linearization $R$ of the minimal surface problem about the Euclidean metric in a bounded smooth domain $\Omega\subset\mathbb{R}^n$, $n\ge2$, with the background minimal surfaces being the Euclidean planes. We show that, in the whole-space Euclidean decomposition, the kernel consists of potential fields and TT fields. For bounded domains, a similar phenomenon appears with additional boundary coupling conditions; in particular, the TT part may be coupled to a harmonic conformal component.

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Haim Grebnev, Plamen Stefanov, Gunther Uhlmann, Hanming Zhou. 2026-06-23. The linearized minimal surfaces problem. https://arxiv.org/abs/2606.24682

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