Author

Guozhen Lu

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Preprint Sep 2026

Sharp $L^2$-stability and gradient stability hierarchies of the $L^2$-Poincar\'e inequalities on Euclidean balls and Gaussian Poincar\'e inequality

We study the sharp $L^2$-Poincar\'e inequalities on Euclidean balls and with respect to the Gaussian measure, and we focus on their stability. In both settings, the sharp constant is the first nonzero eigenvalue of a self-adjoint operator and the set of optimizers is a finite dimensional linear space. Using the spectra...

L. Nguyen, Guo-Zhen Lu · 4 citations

Preprint Oct 2026

The stability of Sharp Poincar\'e and Brascamp--Lieb inequalities with full monomial weights

It was known that the Gaussian measures with monomial weights satisfy the sharp pointwise curvature-dimension condition $CD(1, \infty)$, and consequently they allow us to derive the sharp constant $1$ for the Poincar\'e inequality only with partial monomial weights. In this paper, we first establish the Gaussian measur...

L. Nguyen, Guo-Zhen Lu, A. Russanov · 0 citations

Preprint Aug 2026

Sharp $L^2$-Caffarelli--Kohn--Nirenberg and weighted Poincar\'e inequalities on half-spaces and orthants and their stability

Though the sharp $L^{2}$-Caffarelli--Kohn--Nirenberg (CKN) inequalities have been extensively studied in the entire Euclidean spaces, the corresponding problem on domains whose boundary contains the origin remains largely unexplored. We investigate the sharp $L^{2}$-CKN inequalities on half-spaces and orthants $\mathbb...

L. Nguyen, Yukta Lodha, Guo-Zhen Lu et al. · 4 citations