论文标题
Minkowski空间中$σ_K$曲率流量的全部自我膨胀者
Entire self-expanders for power of $σ_k$ curvature flow in Minkowski space
论文作者
论文摘要
In [19], we prove that if an entire, spacelike, convex hypersurface $\mathcal{M}_{u_0}$ has bounded principal curvatures, then the $σ_k^{1/α}$ (power of $σ_k$) curvature flow starting from $\mathcal{M}_{u_0}$ admits a smooth convex solution $ u $ for $ t> 0。此外，在重新进行续订后，该流量会收敛到一个suffander $ \ tilde {\ mathcal {\ Mathcal {m}} = \ {（x，x，x，x，\ tilde {u}（x）（x）（x）） $σ_K（κ[\ tilde {\ Mathcal {m}}]）=（ - \ weft <x_0，ν_0\ right>）^α。在本文中，我们填补了空白。
In [19], we prove that if an entire, spacelike, convex hypersurface $\mathcal{M}_{u_0}$ has bounded principal curvatures, then the $σ_k^{1/α}$ (power of $σ_k$) curvature flow starting from $\mathcal{M}_{u_0}$ admits a smooth convex solution $u$ for $t>0.$ Moreover, after rescaling, the flow converges to a convex self-expander $\tilde{\mathcal{M}}=\{(x, \tilde{u}(x))\mid x\in\mathbb{R}^n\}$ that satisfies $σ_k(κ[\tilde{\mathcal{M}}])=(-\left<X_0, ν_0\right>)^α.$ Unfortunately, the existence of self-expander for power of $σ_k$ curvature flow in Minkowski space has not been studied before. In this paper, we fill the gap.
