AI 中文总结
该研究证明了满足特定条件的带奇点极小曲面出发的Brakke流存在非唯一性，且无需假设奇点处切锥的唯一性，得到了相关曲面的动力学不稳定性。
AI 中文摘要
我们证明了：若在某奇点处，当尺度趋于零时，Γ₀⊂ℝⁿ⁺¹与n维平面的尺度不变L²距离的上极限足够小，则存在一条从Γ₀出发的真正随时间变化的Brakke流，其关联的重数1的varifold是平稳的。这得到了Stuvard和Tonegawa新近提出的Γ₀的动力学不稳定性，进而得到从Γ₀出发的Brakke流的非唯一性。我们结果的一个显著特点是，它无需假设奇点处切锥的唯一性即可成立。
英文摘要
We prove the existence of a genuinely time-dependent Brakke flow starting from $Γ_0 \subset \mathbb{R}^{n+1}$ whose associated multiplicity-one varifold is stationary, provided that, at some singular point, the scale-invariant $L^2$ distance of $Γ_0$ from an $n$-dimensional plane has sufficiently small limsup as the scale tends to zero. This yields the dynamical instability of $Γ_0$, a notion recently introduced by Stuvard and Tonegawa, and hence the non-uniqueness of Brakke flows starting from $Γ_0$. A notable feature of our result is that it holds without assuming the uniqueness of tangent cones at the singular point.
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