Given a complete, 3-dimensional, asymptotically flat initial data set for the Einstein-Maxwell equations with vanishing magnetic field, we show that there exists a small universal constant $\mathcal{C}$ such that $m\geq\mathcal{C}(\sqrt{\mathcal{A}/(16\pi)}+\mathcal{Q}^2\sqrt{\pi/\mathcal{A}}\,)$. An analogous statement holds for asymptotically hyperboloidal initial data sets with the ADM mass replaced by hyperbolic energy. Under the additional assumption of axisymmetry, the inequality may be further strengthened to include angular momentum. These results extend the Penrose-type inequalities recently obtained by Allen-Bryden-Kazaras-Khuri to the charged setting.
We develop a new convex-integration scheme, inspired by \cite{BCK26}, for the inviscid surface quasi-geostrophic equation on the two-dimensional torus. For the explicit, nonoptimized exponent $\bar p=\frac{4}{3}+10^{-5},$ we prove a flexibility theorem for weak solutions in the standard momentum formulation with active...
The compact four-dimensional manifold $\mathbb{CP}_2\# 3\overline{\mathbb{CP}_2}$ is known to admit a toric K\"ahler-Einstein metric $g_{\text{KE}}$, but the metric is not known in closed form, which makes it difficult to draw conclusions about its geometry. In this article, we use a combination of analytic and compute...
Timothy Buttsworth, William C. Hadden, Elli Heyes et al.· 1 citation
We establish sharp Sobolev-type geometric inequalities on $\mathbb{S}^n$ involving the total $\sigma_k$-curvatures $\int_{\mathbb{S}^n}\sigma_k(g)\,dv_g$. These results extend the optimal inequalities of Guan--Wang~\cite{GWDuke} from the cone $\mathcal{C}_k$ to the strictly larger cone $\mathcal{C}_{k-1}$, thereby enla...
For each positive integer $N$, we construct global spectral group actions for the defocusing and focusing nonlinear Schr\"odinger hierarchies on initial-data classes containing $W^{2N+1,\infty}(\mathbb R)$. For $N\ge2$, the quadratic flow gives global classical cubic NLS solutions. The construction extends the Sato--Se...
S. Kotani, Yi-Qian Wang, Jia-Hao Xu et al.· 1 citation
A compact complex manifold has the bounded mass property if, for one (equivalently, every) Hermitian form $\omega$, the masses $\int_X(\omega+\mathrm{dd}^{\mathrm{c}}\varphi)^n$ are uniformly bounded over all smooth $\varphi$ with $\omega+\mathrm{dd}^{\mathrm{c}}\varphi>0$. We prove that this property fails on the Hopf...
We prove the exact asymptotics of the multidimensional normalized $L^1$ Nikolskii constant \[ \mathcal L^*(d)=\Bigl(\frac{\pi}{2}+o(1)\Bigr)2^{-d}, \quad d\to\infty. \] In addition, for each fixed dimension we obtain asymptotics for the positive zeros of the extremal function $\varphi_d$, and determine their limiting d...
D. Gorbachev· 0 citations
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