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arXiv · 2108.13347

Minimal surfaces in Euclidean spaces by way of complex analysis

Franc Forstneric
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Abstract

This is an expanded version of my plenary lecture at the 8th European Congress of Mathematics in Portoro\v{z} on 23 June 2021. The main part of the paper is a survey of recent applications of complex-analytic techniques to the theory of conformal minimal surfaces in Euclidean spaces. New results concern approximation, interpolation, and general position properties of minimal surfaces, existence of minimal surfaces with a given Gauss map, and the Calabi-Yau problem for minimal surfaces. To be accessible to a wide audience, the article includes a self-contained elementary introduction to the theory of minimal surfaces in Euclidean spaces.

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Franc Forstneric. 2021-08-30. Minimal surfaces in Euclidean spaces by way of complex analysis. https://arxiv.org/abs/2108.13347

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