4 problems

Let $\Gamma\subset\mathbb{R}^3$ be a simple closed curve. Say that $\Gamma$ has total curvature at most $4\pi$ if its total curvature is at most $4\pi$, and say that it is extreme…

Optimal-threshold conjecture. These criteria yield the optimal thresholds in dimension $n\geq3$ for many concrete $p$-elastic flows studied in the literature. The conjecture concer…

Let … spanning an $(n-1)$-dimensional compact manifold … . This proposes a higher-dimensional extension of the Ekholm–White–Wienholtz theorem; the source presents it as a tempting…

Let a Lagrangian mean curvature flow start from embedded initial data, and suppose that it becomes immersed before its singular time. Embeddedness-loss conjecture. The flow must ha…