5 problems

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…

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…

Non-smooth warped-product conjecture. Then the $N$-warped product $B\times^N_f F$ satisfies $CD((N+d-1)K,N+d)$.