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Corpus ID: 119326810

Min-max theory for free boundary minimal hypersurfaces I - regularity theory

@article{Li2016MinmaxTF,
title={Min-max theory for free boundary minimal hypersurfaces I - regularity theory},
author={M. Li and X. Zhou},
journal={arXiv: Differential Geometry},
year={2016}
}

In 1960s, Almgren initiated a program to find minimal hypersurfaces in compact manifolds using min-max method. This program was largely advanced by Pitts and Schoen-Simon in 1980s when the manifold has no boundary. In this paper, we finish this program for general compact manifold with nonempty boundary. As a result, we prove the existence of a smooth embedded minimal hypersurface with free boundary in any compact smooth Euclidean domain. An application of our general existence result combined… CONTINUE READING