18 citations · 44 across the 9 of their papers we have counts for
13 papers
Three isometrically equivalent models of the Finsler-Poincaré disk
Ágnes Mester, Alexandru Kristály
We present the isometry between the 2-dimensional Funk model and the Finsler-Poincaré disk. Then, we introduce the Finslerian Poincaré upper half plane model, which turns out to be…
Sharp Morrey-Sobolev inequalities and eigenvalue problems on Riemannian-Finsler manifolds with nonnegative Ricci curvature
Alexandru Kristály, Ágnes Mester, Ildikó I. Mezei
Combining the sharp isoperimetric inequality established by Z. Balogh and A. Kristály [Math. Ann., in press, doi:10.1007/s00208-022-02380-1] with an anisotropic symmetrization argu…
A bipolar Hardy inequality on Finsler manifolds
Ágnes Mester, Alexandru Kristály
We establish a bipolar Hardy inequality on complete, not necessarily reversible Finsler manifolds. We show that our result strongly depends on the geometry of the Finsler structure…
Poincaré's lemma on some non-Euclidean structures
Alexandru Kristály
In this paper we prove the Poincaré lemma on some -dimensional corank 1 sub-Riemannian structures, formulating the necessarily and sufficiently 'cur…
Nodal solutions for the fractional Yamabe problem on Heisenberg groups
Alexandru Kristály
We prove that the fractional Yamabe equation on the Heisenberg group has sequences of nodal (sign-changing) wea…
Geometric inequalities on Heisenberg groups
Zoltán M. Balogh, Alexandru Kristály, Kinga Sipos
We establish geometric inequalities in the sub-Riemannian setting of the Heisenberg group . Our results include a natural sub-Riemannian version of the celebrated curv…
Singular Poisson equations on Finsler-Hadamard manifolds
Csaba Farkas, Alexandru Kristály, Csaba Varga
In the first part of the paper we study the reflexivity of Sobolev spaces on non-compact and not necessarily reversible Finsler manifolds. Then, by using direct methods in the calc…
Sharp Morrey-Sobolev inequalities on complete Riemannian Manifolds
Alexandru Kristály
Two Morrey-Sobolev inequalities (with support-bound and bound, respectively) are investigated on complete Riemannian manifolds with their sharp constants in . We…
What do `convexities' imply on Hadamard manifolds?
Alexandru Kristály, Chong Li, Genaro Lopez +1
Various results based on some convexity assumptions (involving the exponential map along with affine maps, geodesics and convex hulls) have been recently established on Hadamard ma…
Metric measure spaces supporting Gagliardo-Nirenberg inequalities: volume non-collapsing and rigidities
Alexandru Kristály
Let be a metric measure space which satisfies the Lott-Sturm-Villani curvature-dimension condition for some and …
Sharp uncertainty principles on Riemannian manifolds: the influence of curvature
Alexandru Kristály
We present a rigidity scenario for complete Riemannian manifolds supporting the Heisenberg-Pauli-Weyl uncertainty principle with the sharp constant in (shortly, sharp…
A constructive approach to triangular trigonometric patches
Ágoston Róth, Imre Juhász, Alexandru Kristály
We construct a constrained trivariate extension of the univariate normalized B-basis of the vector space of trigonometric polynomials of arbitrary (finite) order n defined on any c…
Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applications
Alexandru Kristály, Shin-ichi Ohta
We prove that if a metric measure space satisfies the volume doubling condition and the Caffarelli-Kohn-Nirenberg inequality with the same exponent , then it has exactly t…