3 problems

Let $N$ be an oriented $\mathbb{S}^1$-bundle over a closed, oriented $3$-manifold $M$. The bundle has an Euler class, and suppose this Euler class is even. The main result gives a…

An Engel structure is a maximally non-integrable rank-2 distribution $\mathcal{D} \subseteq TN$ on a $4$-manifold $N$. Such structures have no local invariants beyond their local n…

Global minimality conjecture. The set $\Omega$ is a global minimum among all possible immersed surfaces sharing the same boundary $\partial\Omega$.