Min-max theory for free boundary minimal hypersurfaces I: regularity theory
Publication in refereed journal

香港中文大學研究人員

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摘要In 1960s, Almgren initiated a program to find minimal hypersurfaces in Riemannian manifolds using min-max method. This program was largely advanced by Pitts and Schoen-Simon in 1980s when the manifold is compact without boundary. In this paper, we finish this program for general compact manifold with non-empty boundary. As a corollary, we establish the existence of a smooth embedded minimal hypersurface with non-empty free boundary in any compact smooth Euclidean domain. An application of our general existence result combined with the work of Marques and Neves shows that for any compact Riemannian manifolds with nonnegative Ricci curvature and convex boundary, there exist infinitely many properly embedded minimal hypersurfaces with non-empty free boundary.
出版社接受日期12.03.2019
著者Martin Man-chun Li, Xin Zhou
期刊名稱Journal of Differential Geometry
出版年份2021
月份7
卷號118
期次3
出版社International Press
頁次487 - 553
國際標準期刊號0022-040X
電子國際標準期刊號1945-743X
語言美式英語

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