Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 70, No. 1, pp. 33-66, 2020

Hyperbolic inverse mean curvature flow

Jing Mao, Chuan-Xi Wu, Zhe Zhou

Received April 3, 2018. Published online September 19, 2019.

Abstract: We prove the short-time existence of the hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of $\mathbb{R}^{n+1}$ ($n\ge2$) is mean convex and star-shaped. Several interesting examples and some hyperbolic evolution equations for geometric quantities of the evolving hypersurfaces are shown. Besides, under different assumptions for the initial velocity, we can get the expansion and the convergence results of a hyperbolic inverse mean curvature flow in the plane $\mathbb{R}^2$, whose evolving curves move normally.

Keywords: evolution equation; hyperbolic inverse mean curvature flow; short time existence

Classification MSC: 58J45; 58J47

DOI: 10.21136/CMJ.2019.0162-18

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Jing Mao (corresponding author), Chuan-Xi Wu, Zhe Zhou, Faculty of Mathematics and Statistics, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University, Wuhan, 430062, P. R. China, e-mail: jiner120@163.com, jiner120@tom.com

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