6 problems

Coercivity conjecture. The coercivity condition is generally satisfied: there exist constants $c_{\mathcal{H}_{{K}^E}},c_{\mathcal{H}_{{K}^A}}>0$ such that

Aubin's conjecture. There exist positive constants $A$ and $B$ such that

For the $n$-lump sector of the ${\mathbb{C}}{{P}}^1$ model on $S^2$, let $\tau^{eq}(\mu)$ be the equivariant coercivity constant for the map $\phi:z\mapsto \mu z^n$, with…

Let ${\sf Hess}^{eq}$ denote the equivariant Hessian in the $n$-lump sector of the ${\mathbb{C}}{{P}}^1$ model on $S^2$. Global equivariant coercivity conjecture. We conjecture tha…

Let $D$ be an operator, let $V$ be the ambient space, and let $a(\cdot,\cdot)$ be a bilinear operator. Define … where $\epsilon>0$ is small. Suppose that $a(u,v)$ is coercive on…

Non-coercivity conjecture. The functional $\hat{\mycal E}_\infty$ is not coercive on $\hat X_\infty$.