November 8, 2025Open Access

Minimally embedded Riemann surfaces in S³ and the conformal deformation of their metrics

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Conformal deformation of metrics improves understanding of minimal embeddings in Riemann surfaces, especially in S^3.
Scalar curvature plays a vital role in relating area metrics and embeddings of Riemann surfaces into S^3.
Diffeomorphism insights highlight the uniqueness of certain surfaces like the Lawson surface versus the Clifford torus.
The findings may redefine approaches to characterizing orientable Riemannian surfaces with minimal embeddings.

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Implication

We demonstrate minimal isometric embedding deformations in Riemann surfaces, suggesting implications for scalar curvature and diffeomorphic properties.

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Santiago R. Simanca (2025) studied this question.

synapsesocial.com/papers/690e8b75a5b062d7a4e7394f https://doi.org/10.48550/arxiv.2510.02555

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Implication

We demonstrate minimal isometric embedding deformations in Riemann surfaces, suggesting implications for scalar curvature and diffeomorphic properties.

Minimally embedded Riemann surfaces in S³ and the conformal deformation of their metrics

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Discussion

Implication

Cite This Study

Minimally embedded Riemann surfaces in S³ and the conformal deformation of their metrics

Key Points

Discussion

Implication

Cite This Study

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