Minimal surfaces in Euclidean spaces by way of complex analysis
Differential Geometry
2024-11-01 v2
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.
Keywords
Cite
@article{arxiv.2108.13347,
title = {Minimal surfaces in Euclidean spaces by way of complex analysis},
author = {Franc Forstneric},
journal= {arXiv preprint arXiv:2108.13347},
year = {2024}
}
Comments
To appear in Proceedings of the 8th European Congress of Mathematics