极小曲面Gauss像的值分布

The value distribution under the Gauss map for a minimal submanifold

本文概述了欧氏空间中极小子流形Gauss像值分布问题的最新研究进展,包括高维极小超曲面Gauss像分布的丘成桐问题,以及高余维极小子流形的Lawson-Osserman问题;介绍了作者及其合作者近年来在这两方面的研究结果和研究方法,并提出了进一步的相关研究问题.

In this paper, some new aspects for the value distribution of the image under the Gauss map for a minimal submanifold in Euclidean space are reviewed, including Yau＇s problem for minimal hypersurfaces and Lawson-Osserman＇s problem for higher codimension. Among them the author＇s joint work with his collaborators in recent years is described.