Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^4$
- Resource Type
- Working Paper
- Authors
- Alarcon, Antonio; Lopez, Francisco J.
- Source
- Subject
- Mathematics - Differential Geometry
Mathematics - Complex Variables
- Language
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.