5 problems

Let the Trudinger-type inequality on the two-dimensional upper half space be the inequality established above for functions on $B^+_{R_0}$ with weighted measure $t^{\beta}\,dx\,dt$…

Let $J_{\alpha}$ be the functional on $H^2(\mathbb{S}^6)$ defined by … where $\mathrm{d}w$ is normalized Lebesgue measure and $P_6=-\Delta(-\Delta+4)(-\Delta+6)$. Let … For every…

Strictness and convergence conjecture. The inequality $\gamma\leq n+1$ in the preceding theorem is strict, namely $\gamma<n+1$. Moreover, $\phi_j$ converges weakly to $g_{\Omega}$.

Let $X$ be a Fano manifold with $[\omega]=c_{1}(-K_{X})$, and let $\mathcal{H}(X,\omega)$ denote the relevant space of normalized $\omega$-plurisubharmonic functions. Let $\xi_{n}$…

Symmetry-free Moser–Trudinger conjecture. The symmetry assumption in the preceding theorem may be removed; that is, the displayed inequality with the sharp multiplicative constant…