8 problems

Weighted Riemannian warped-product curvature conjecture. The $N$-warped product of $B$, $F$, and $f$ satisfies $\mathsf{CD}(K(N+d-1),N+d)$ if $(B,f^{N+d}\operatorname{vol}_B)$ is a…

Metric-measure-space extension conjecture. The results should also hold in more general metric measure spaces with synthetic curvature bounds.

Lorentzian warped-product timelike curvature-dimension conjecture. If $f”-Kf\leq0$ and $(F,d_F,\operatorname{m}_F)$ is non-branching and satisfies $\mathsf{CD}(K_F(N-1),N)$, then t…

Lorentzian warped-product curvature conjecture. The Lorentzian warped product $-I\times_fF$ has timelike CBB by $K$ if and only if $f$ is $-Kf$-concave and $F$ has CBB by $K_F$. Th…

Noncollapsed RCD warped-product conjecture. The $N$-warped product of $B$, $F$, and $f$ satisfies $\mathsf{CD}(K(N+d-1),N+d)$ if $B^\dagger$ is a noncollapsed…

Let $X$ be an essentially non-branching metric-measure space, and let $C(X)$ denote its Euclidean $N$-cone. Euclidean cone curvature-dimension conjecture. The Euclidean $N$-cone…

Let $B$ be a metric-measure base of dimension $d$, let $F$ be an essentially non-branching metric-measure space, and let $f$ be a Lipschitz nonnegative warping function. Let…

Let $B\times_f^{N}F$ be an $N$-warped product of a Riemannian manifold $B$, a positive warping function $f$, and a weighted Riemannian manifold $F$. The weighted semi-Riemannian an…