arXiv subjects

Alexandru Pîrvuceanu

Publications and source records attributed to Alexandru Pîrvuceanu.

3 recordsLinked to original sources

arXiv2026

Quantitative stability for Bakry--Émery log-Sobolev and Talagrand inequalities

We establish quantitative $L^1$-stability estimates for the Bakry--Émery log-Sobolev and Talagrand inequalities with a universal exponent of 1/19 governing the corresponding deficits. Our approach relies on a Maurey-type argument combined with stability estimates for the Prékopa--Leindler inequality. In the radial setting, the exponent of both deficits can be improved to $1/2,$ which turns out to be optimal. As an application, we establish an estimate for the hypercontractivity deficit of the Hopf--Lax semigroup in the Bakry--Émery setting. In particular, these stability results provide elementary characterizations for the equality cases in the previously mentioned inequalities.

math.AP↗

arXiv2026

$\bf{S^1}$-index theory for the Lorentz force equation

In this paper we prove that the $S^1$-invariance of the Poincaré action functional associated to the Lorentz force equation gives the existence of multiple critical points which are periodic solutions with a fixed period. To do this, we prove an abstract multiplicity result which is based upon the Lusternik-Schnirelman method with the $S^1$-index. The corresponding result in the context of the Fadell-Rabinowitz index is proved in Ekeland and Lasry (Ann. Math., 112 (1980)). The main feature of our abstract result is that it allows us to consider nonsmooth functionals satisfying only a weak compactness condition well adapted to the Poincaré functional.

math.AP↗

arXiv2025

Hypercontractivity of the heat flow on ${\sf RCD}(0,N)$ spaces: sharpness and rigidities

The main goal of the present paper is to provide sharp hypercontractivity bounds of the heat flow $({\sf H}_t)_{t\geq 0}$ on ${\sf RCD}(0,N)$ metric measure spaces. The best constant in this estimate involves the asymptotic volume ratio, and its optimality is obtained by means of the sharp $L^2$-logarithmic Sobolev inequality on ${\sf RCD}(0,N)$ spaces and a blow-down rescaling argument. Equality holds in this sharp estimate for a prescribed time $t_0>0$ and a non-zero extremizer $f$ if and only if the ${\sf RCD}(0,N)$ space has an $N$-Euclidean cone structure and $f$ is a Gaussian whose dilation factor is reciprocal to $t_0$, up to a multiplicative constant. Applications include an extension of Li's rigidity result, almost rigidities, as well as topological rigidities of non-collapsed ${\sf RCD}(0, N)$ spaces. Our results are new even on complete Riemannian manifolds with non-negative Ricci curvature.

math.AP↗