arXiv subjects
Publications and source records attributed to Yaozhong W. Qiu.
We prove an $L^2$-stability estimate for the variance Brascamp-Lieb inequality [J. Funct. Anal. 22 (4), 366-389 (1976)] by bootstrapping the recent $L^1$-stability theorem of Machado and Ramos [arXiv:2511.22636] under an additional assumption, which we call the super-Brascamp-Lieb inequality, of independent interest.
We continue the program initiated by [J. Éc. Polytech., Math. 12, 1083-1160 (2025)] and show that the Pleijel theorem holds unconditionally on all but four $H$-type groups.
We prove the existence of almost isoperimetric extremisers for two classes of probability measures defined respectively on the Grushin space and a stratified Lie group. It turns out such extremisers can be regarded as a type of anisotropic half-space.
We prove $q$-super-Poincaré inequalities, $q \in [1, 2]$, for a class of exponential power type probability measures defined in terms of a norm in a number of subelliptic settings, primarily on stratified Lie groups but also in the Grushin and Heisenberg-Greiner settings. Our results include generically optimal isoperimetric inequalities for such probability measures.
We continue the $U$-bound program initiated in [J. Funct. Anal. 258, 814-851 (2010)] and prove super-Poincaré inequalities for a class of subelliptic probability measures defined on Métivier groups, the main ingredient in the proof being a Hardy-type inequality. In doing so, we recover and extend some previous results from the probabilistic viewpoint.
We show a symmetric Markov diffusion semigroup satisfies a weighted contractivity condition if and only if a $L^2$-Hardy inequality holds, and we give a Bakry-Émery type criterion for the former. We then give some applications.
We continue the program first initiated in [Geom. Funct. Anal. 26, 288-305 (2016)] and develop a modification of the technique introduced in that paper to study the spectral asymptotics, namely the Riesz means and eigenvalue counting functions, of functional difference operators $\smash{H_0 = \mathcal F^{-1} M_{\cosh(ξ)} \mathcal F}$ with potentials of the form $\smash{W(x) = \lvert{x\rvert}^pe^{\lvert{x\rvert}^β}}$ for either $β= 0$ and $p > 0$ or $β\in (0, 2]$ and $p \geq 0$. We provide a new method for studying general potentials which includes the potentials studied in [Geom. Funct. Anal. 26, 288-305 (2016)] and [J. Math. Phys. 60, 103505 (2019)]. The proof involves dilating the variance of the gaussian defining the coherent state transform in a controlled manner preserving the expected asymptotics.