Nonhomogeneous inverse mean curvature flow in Euclidean space

2020 ◽  
Vol 148 (10) ◽  
pp. 4557-4571
Author(s):  
Li Chen ◽  
Xi Guo ◽  
Qiang Tu
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Inverse Mean Curvature Flow

scholarly journals Hyperbolic inverse mean curvature flow

2019 ◽  
Vol 70 (1) ◽  
pp. 33-66
Author(s):  
Jing Mao ◽  
Chuan-Xi Wu ◽  
Zhe Zhou
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Inverse Mean Curvature Flow

scholarly journals Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Ruiwei Xu ◽  
Linfen Cao
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Indefinite Metric ◽  
Bernstein Theorem ◽  
Strictly Convex ◽  
Convex Solution

Letf(x)be a smooth strictly convex solution ofdet(∂2f/∂xi∂xj)=exp(1/2)∑i=1nxi(∂f/∂xi)-fdefined on a domainΩ⊂Rn; then the graphM∇fof∇fis a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean spaceRn2nwith the indefinite metric∑dxidyi. In this paper, we prove a Bernstein theorem for complete self-shrinkers. As a corollary, we obtain if the Lagrangian graphM∇fis complete inRn2nand passes through the origin then it is flat.

scholarly journals Life-Span of Classical Solutions to Hyperbolic Inverse Mean Curvature Flow

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Zenggui Wang
Keyword(s):  
Cauchy Problem ◽  
Life Span ◽  
Hyperbolic System ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Classical Solutions ◽  
Quasilinear Hyperbolic System ◽  
Inverse Mean Curvature Flow ◽  
The Cauchy Problem

In this paper, we investigate the life-span of classical solutions to hyperbolic inverse mean curvature flow. Under the condition that the curve can be expressed in the form of a graph, we derive a hyperbolic Monge–Ampère equation which can be reduced to a quasilinear hyperbolic system in terms of Riemann invariants. By the theory on the local solution for the Cauchy problem of the quasilinear hyperbolic system, we discuss life-span of classical solutions to the Cauchy problem of hyperbolic inverse mean curvature.

scholarly journals Rigidity results and topology at infinity of translating solitons of the mean curvature flow

2017 ◽  
Vol 19 (06) ◽  
pp. 1750002 ◽  
Author(s):  
Debora Impera ◽  
Michele Rimoldi
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Minimal Hypersurfaces ◽  
Rigidity Results ◽  
And Topology ◽  
The Mean ◽  
Translating Solitons

In this paper, we obtain rigidity results and obstructions on the topology at infinity of translating solitons of the mean curvature flow in the Euclidean space. Our approach relies on the theory of [Formula: see text]-minimal hypersurfaces.

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