5 problems

Let $\Lambda_n:= \sup_{U \in \mathcal{S}\mathcal{C}(\mathbb{R}^n)} \lambda_1$ be the supremum of the first stability eigenvalue over singular minimizing cones in $\mathbb{R}^n$, an…

Let $C_{\text{\tiny{BE}}}$ denote the best Bianchi–Egnell constant for the one-dimensional fractional Sobolev inequality, and let $C_{\text{\tiny{BE}}}^{\text{\tiny{loc}}}$ denote…

Let $X$ be a compact Kähler manifold, let $\Omega$ be a Lorentzian class of dimension $d$ on $X$, and let $\alpha,\beta$ be big nef classes on $\Omega$. Define…

Let $X$ be a compact Kähler manifold of dimension $n$, and let $\alpha,\beta\in\operatorname{Mov}^1(X)$ be big movable classes. Let $F(\alpha,\beta)$ denote their relative asymmetr…

The paper studies quantitative stability bounds for optimal transport inequalities and maps, with the Euclidean arguments relying on functional inequalities such as Gagliardo–Niren…