A dual simple proof of the classical Bernstein and Calabi–Bernstein theorems
Open Access
- 16 July 2025
- journal article
- Published by Finnish Mathematical Society in Annales Fennici Mathematici
- Vol. 50 (2) , 511–518
Abstract
In this note, we present a short and simple proof of both the Bernstein theorem and the Calabi–Bernstein theorem, which allows us to visualize both the common features and the remarkable differences between the two results. The proofs are based on the construction of conformal metrics that ensure the parabolicity of the surfaces. Consequently, they do not rely on complex analysis.Keywords
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