6 papers
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…