8 problems

Let $1\leq l<k$ and consider the general Hessian quotient equation … Let $u$ be a solution on a closed Riemannian manifold $(M,g)$ endowed with a symmetric $(2,0)$ tensor $\chi$. C…

Let $M$ be a connected, closed Riemannian manifold with metric $g$, and let $\chi$ be a symmetric $(2,0)$ tensor on $M$. Suppose that there is an admissible function $v\in C^4(M)$…

Ren–Wang's concavity conjecture. For every $\xi=(\xi_1,\ldots,\xi_n)\in\mathbb{R}^n$,

Strict convexity conjecture. If $r_f(x)$ is strictly right-Noetherian, then the level set $\{f=0\}$ is strictly convex; equivalently, the Hessian matrix

Let $\overrightarrow{a}=(a_0,a_1,\ldots,a_p)\in(\mathbb{R}_+)^{p+1}$ and define … Here $\Gamma_n$ denotes the Gårding cone. Concavifying-function conjecture. There exists…

Let $(M^{2n},g,J_\pm)$ be a generalized Kähler structure satisfying $[J_+,J_-]=0$. Let $\mathcal H$ be the space of formally generalized Kähler classes, and let $P$ be the associat…

CR $k$-Yamabe existence conjecture. If

CR sphere k-Yamabe conjecture. If the pseudohermitian structure $\widetilde{\theta}=e^{2u}\hat{\theta}\in[\hat{\theta}]_{+}$ has constant pseudohermitian $k$-curvature, then…