# Inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

@inproceedings{Gao2021InverseMC, title={Inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space \$\mathbb\{R\}^\{n+1\}\_\{1\}\$}, author={Ya Gao and Jing Mao}, year={2021} }

In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane H (1), of center at origin and radius 1, in the (n+1)dimensional Lorentz-Minkowski space R 1 along the inverse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of hyperbolic plane…

## 5 Citations

### Inverse Gauss curvature flow in a time cone of Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

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In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane H (1), of center at origin and radius 1, in the (n + 1)-dimensional…

### Pogorelov type estimates for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

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Let Ω be a bounded domain (with smooth boundary) on the hyperbolic plane H (1), of center at origin and radius 1, in the (n + 1)-dimensional Lorentz-Minkowski space R n+1 1 . In this paper, by using…

### The Dirichlet problem for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

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In this paper, under suitable settings, we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in LorentzMinkowski space R…

### Curvature estimates for spacelike graphic hypersurfaces in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

- Mathematics
- 2021

In this paper, we can obtain curvature estimates for spacelike admissible graphic hypersurfaces in the (n + 1)-dimensional Lorentz-Minkowski space R 1 , and through which the existence of spacelike…

### An anisotropic inverse mean curvature flow for spacelike graphic curves in Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$

- Mathematics
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In this paper, we consider the evolution of spacelike graphic curves defined over a piece of hyperbola H (1), of center at origin and radius 1, in the 2-dimensional LorentzMinkowski plane R21 along…

## References

SHOWING 1-10 OF 58 REFERENCES

### A class of inverse curvature flows for star-shaped hypersurfaces evolving in a cone

- Mathematics
- 2021

Given a smooth convex cone in the Euclidean (n+ 1)-space (n ≥ 2), we consider strictly mean convex hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which…

### On inverse mean curvature flow in Schwarzschild space and Kottler space

- Mathematics
- 2017

In this paper, we first study the behavior of inverse mean curvature flow in Schwarzschild manifold. We show that if the initial hypersurface $$\Sigma $$Σ is strictly mean convex and star-shaped,…

### Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature

- Mathematics
- 1986

which shrink towards the center of the initial sphere in finite time. It was shown in [3], that this behaviour is very typical: If the initial hypersurface M o o R , + 1 is uniformly convex, then the…

### Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere

- Mathematics
- 2016

We prove a rigidity result in the sphere which allows us to generalize a result about smooth convex hypersurfaces in the sphere by Do Carmo-Warner to convex $C^2$-hypersurfaces. We apply these…

### Long-time existence and convergence of graphic mean curvature flow in arbitrary codimension

- Mathematics
- 2002

Abstract.Let f:Σ1↦Σ2 be a map between compact Riemannian manifolds of constant curvature. This article considers the evolution of the graph of f in Σ1×Σ2 by the mean curvature flow. Under suitable…

### Inverse Mean Curvature Flow for Star-Shaped Hypersurfaces Evolving in a Cone

- Mathematics
- 2013

For a given convex cone we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicular. The evolution of those…

### Flow of nonconvex hypersurfaces into spheres

- Mathematics
- 1990

The flow of surfaces by functions of their principal curvatures has been intensively studied. It started with the work of Brakke [1], who used the formalism of geometric measure theory; a more…

### Convex Mean Curvature Flow with a Forcing Term in Direction of the Position Vector

- Mathematics

A smooth, compact and strictly convex hypersurface evolving in R along its mean curvature vector plus a forcing term in the direction of its position vector is studied in this paper. We show that the…

### The inverse mean curvature flow and the Riemannian Penrose Inequality

- Mathematics
- 2001

Let M be an asymptotically flat 3-manifold of nonnegative scalar curvature. The Riemannian Penrose Inequality states that the area of an outermost minimal surface N in M is bounded by the ADM mass m…

### Inverse mean curvature flow inside a cone in warped products

- Mathematics
- 2017

Given a convex cone in the \emph{prescribed} warped product, we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone…