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Minimal Surfaces as Entropy-Density Minimizers: A Classical Investigation

Year: 2025

Type: article

Abstract: This study proposes that minimal surfaces not only minimize area but also minimize a natural entropy-density functional based on the mean curvature squared. By analyzing surfaces such as the catenoid, helicoid, and Enneper surface, we confirm that minimal surfaces achieve zero entropy-density while non-minimal surfaces (such as spheres, ellipsoids, and paraboloids) exhibit significant positive entropy-density. This offers a new structural variational principle for understanding minimal surfaces in differential geometry.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.15285151

Author: Fernandes, Ricardo Miguel Machado

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6912054030

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