A note on the Gauss curvature flow (Q2822151)

The purpose of the present article, is to obtain a uniform lower bound of \(\varphi^*\), a solution of the associated normalized evolution equation of NEWLINE\[NEWLINE\displaystyle\frac{\partial \varphi (x,t)}{\partial t}=-\mathcal{K}(x,t)\nu(x,t),\;\varphi(\cdot,0)=\varphi_0(\cdot),NEWLINE\]NEWLINE such that \(\varphi(\cdot,\cdot)\) is a smooth map on \(\partial K\times [0,T)\) and taking values in \(\mathbb R^n\), \(\partial K\) is the boundary of a convex body \(K\), \(\mathcal{K}(x,t)\) stands for the Gauss curvature of \(\varphi(\partial K,t)\) at the point where the outer unit normal is \(\nu(x,t)\), and \(T\) is the maximal time where the flow exists.