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arXiv · 2410.12131

The planar Plateau's problem via capillarity

Kennedy Obinna Idu
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Abstract

The Plateau's problem seeks to determine a surface of minimal area which spans a given boundary. It is widely studied for its varied mathematical formulations, applications and relevance to physical models such as soap films. We revisit the problem and study a soap film model in the spirit of capillarity formulations in two dimensions. Our approach introduces a nonlocal geometric potential in the variational length minimization scheme. This incorporates effects of thickness of soap films and provides insight into addressing the so-called collapsing phenomenon and other observable physical phenomena and properties.

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Kennedy Obinna Idu. 2024-10-16. The planar Plateau's problem via capillarity. https://arxiv.org/abs/2410.12131

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