# Research

S. Mui, On the $L^{p}$ Aleksandrov Problem for negative $p$, Adv. Math, 408 (2022). link
We prove the existence of a solution to the $L^{p}$ Aleksandrov problem or the case of given even measures and $p ∈ (−1, 0)$. Furthermore, a sufficient measure concentration condition was provided for the case of $p ≤ −1$, again provided that the given measure is even.

S. Mui, On the $L^{p}$ dual Minkowski problem for $-1 < p < 0$, in preparation.
We prove the existence of a solution to the $L^{p}$ dual Minkowski problem for the case of $q < p+1$, $-1 < p < 0$, and $p \neq q$ for even measures.