Junqi Lai

Singular Rotational Self-Similar Tori for Odd $\sigma_k$-Curvature Flows

For every pair of integers $3\leq k<n$ with $k$ odd, we construct a compact embedded rotational torus in $\mathbb{R}^{n+1}$ whose homothetic dilations satisfy the unnormalised $\sigma_k$-curvature flow in a Sobolev almost-everywhere sense. Its profile curve has H\"older regularity $C^{1,1/k}$ and Sobolev regularity $W^...