Hyperbolic inverse mean curvature flow

Jing Mao; Chuan-Xi Wu; Zhe Zhou

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 1, page 33-66
  • ISSN: 0011-4642

Abstract

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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 ℝ n + 1 ( n ≥ 2 ) 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 ℝ 2 , whose evolving curves move normally.

How to cite

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Mao, Jing, Wu, Chuan-Xi, and Zhou, Zhe. "Hyperbolic inverse mean curvature flow." Czechoslovak Mathematical Journal 70.1 (2020): 33-66. <http://eudml.org/doc/297330>.

@article{Mao2020,
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 $\mathbb \{R\}^\{n+1\}$ ($n\ge 2$) 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.},
author = {Mao, Jing, Wu, Chuan-Xi, Zhou, Zhe},
journal = {Czechoslovak Mathematical Journal},
keywords = {evolution equation; hyperbolic inverse mean curvature flow; short time existence},
language = {eng},
number = {1},
pages = {33-66},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Hyperbolic inverse mean curvature flow},
url = {http://eudml.org/doc/297330},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Mao, Jing
AU - Wu, Chuan-Xi
AU - Zhou, Zhe
TI - Hyperbolic inverse mean curvature flow
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 1
SP - 33
EP - 66
AB - 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 $\mathbb {R}^{n+1}$ ($n\ge 2$) 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.
LA - eng
KW - evolution equation; hyperbolic inverse mean curvature flow; short time existence
UR - http://eudml.org/doc/297330
ER -

References

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