7 citations · 8 across the 10 of their papers we have counts for
11 papers
Quantitative stability for Bakry--Émery log-Sobolev and Talagrand inequalities
Alexandru Kristály, Alexandru Pîrvuceanu
We establish quantitative -stability estimates for the Bakry--Émery log-Sobolev and Talagrand inequalities with a universal exponent of 1/19 governing the corresponding defici…
Analysis on asymmetric metric measure spaces: -heat flow, -Laplacian and Sobolev spaces
Alexandru Kristály, Shin-ichi Ohta, Wei Zhao
We investigate geometric analysis on metric measure spaces equipped with asymmetric distance functions. Extending concepts from the symmetric case, we introduce upper gradients and…
Sharp stability in hypercontractivity estimates and logarithmic Sobolev inequalities
Zoltán M. Balogh, Alexandru Kristály
We prove stability results in hypercontractivity estimates for the Hopf--Lax semigroup in and apply them to deduce stability results for the Euclidean -logarithm…
Hypercontractivity of the heat flow on spaces: sharpness and rigidities
Shouhei Honda, Alexandru Kristály, Alexandru Pîrvuceanu
The main goal of the present paper is to provide sharp hypercontractivity bounds of the heat flow on metric measure spaces. The best consta…
Volume growths versus Sobolev inequalities
Alexandru Kristály
The paper deals with fine volume growth estimates on metric measures spaces supporting various Sobolev-type inequalities. Given a generic metric measure space, we first prove a qua…
Logarithmic-Sobolev inequalities on non-compact Euclidean submanifolds: sharpness and rigidity
Zoltán M. Balogh, Alexandru Kristály
The paper is devoted to provide Michael-Simon-type -logarithmic-Sobolev inequalities on complete, not necessarily compact -dimensional submanifolds of the Euclidean spa…
Failure of famous functional inequalities on Finsler manifolds: the influence of -curvature
Alexandru Kristály, Benling Li, Wei Zhao
The validity of functional inequalities on Finsler metric measure manifolds is based on three non-Riemannian quantities, namely, the reversibility, flag curvature and -curvature…
Sharp Hardy inequalities involving distance functions from submanifolds of Riemannian manifolds
Ningwei Cui, Alexandru Kristály, Wei Zhao
We establish various Hardy inequalities involving the distance function from submanifolds of Riemannian manifolds, where the natural weights are expressed in terms of bounds of the…
Sharp Sobolev inequalities on noncompact Riemannian manifolds with via Optimal Transport theory
Alexandru Kristály
In their seminal work, Cordero-Erausquin, Nazaret and Villani [Adv. Math., 2004] proved sharp Sobolev inequalities in Euclidean spaces via Optimal Mass Transportation, raising the…
A generic functional inequality and Riccati pairs: an alternative approach to Hardy-type inequalities
Sándor Kajántó, Alexandru Kristály, Ioan Radu Peter +1
We present a generic functional inequality on Riemannian manifolds, both in additive and multiplicative forms, that produces well known and genuinely new Hardy-type inequalities. F…
Sharp log-Sobolev inequalities in spaces with applications
Zoltán M. Balogh, Alexandru Kristály, Francesca Tripaldi
Given we prove the sharp -log-Sobolev inequality on noncompact metric measure spaces satisfying the condition, where the optimal constant involves the…