A nonexistence result for rotating mean curvature flows in \(\mathbb{R}^4\) (Q6137563)

The paper shows that there are no rotating ancient noncollapsed flows \(M_t \in \mathbb{R}^4\). Here a non-collapsing flow is the flow moving inwards and there is a constant \(\alpha\) where, for each point \(p \in M_t\), there are interior and exterior balls of radius \(\geq \alpha/H(p)\) containing \(p\). In addition, the main result of the paper improves an existing result of the same authors (\textit{W. Du} and \textit{R. Haslhofer}, [Commun. Pure Appl. Math. 77, No. 1, 543--582 (2024; Zbl 1530.35136)]) and with this result one has advantage that the fine-bubble sheet matrix is allowed to be taken independent of time i.e. the bubble-sheet function \(u\) fulfills \[ \lim_{\tau\to -\infty}\left \Vert |\tau|u(\mathbf{y},v,\tau)-\mathbf{y}^{\top}Q\mathbf{y}+2\text{tr}(Q) \right \Vert_{C^k(B_R)}=0, \quad \forall R < \infty, \quad \forall k\in \mathbb{Z}, \] where \(Q\) is a constant symmetric \(2\times2\)-matrix with eigenvalues are quantized to be \(0\) or \(-1/\sqrt{8}\).