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arXiv · 2206.03566

Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^4$

Antonio Alarcon·Francisco J. Lopez
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Abstract

We prove that every open Riemann surface admits a proper embedding into $\mathbb{R}^4$ by harmonic functions. This reduces by one the previously known embedding dimension in this framework, dating back to a theorem by Greene and Wu from 1975.

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Antonio Alarcon, Francisco J. Lopez. 2026-04-09. Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^4$. https://arxiv.org/abs/2206.03566

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