15 papers
On the geometry of irreversible metric-measure spaces: Convergence, Stability and Analytic aspects
Alexandru Kristály, Wei Zhao
The paper is devoted to the study of Gromov-Hausdorff convergence and stability of irreversible metric-measure spaces, both in the compact and noncompact cases. While the compact s…
Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups
Csaba Farkas, Alexandru Kristály, Ágnes Mester
Given a complete non-compact Riemannian manifold with certain curvature restrictions, we introduce an expansion condition concerning a group of isometries of th…
Sobolev inequalities with jointly concave weights on convex cones
Zoltán M. Balogh, Cristian E. Gutiérrez, Alexandru Kristály
Using optimal mass transport arguments, we prove weighted Sobolev inequalities of the form \[\left(\int_E |u(x)|^q\,ω(x) \,dx\right)^{1/q}\leq K_0\,\left(\int_E |\nabla u(x)|^p\,σ(…
Differential inclusions involving oscillatory terms
Alexandru Kristály, Ildikó I. Mezei, Károly Szilák
Motivated by mechanical problems where external forces are non-smooth, we consider the differential inclusion problem \[ \begin{cases} -Δu(x)\in \partial F(u(x))+λ\partial G(u(x))\…
Fundamental tones of clamped plates in nonpositively curved spaces
Alexandru Kristály
We study Lord Rayleigh's problem for clamped plates on an arbitrary -dimensional Cartan-Hadamard manifold with sectional curvature for…
Topological rigidity of compact manifolds supporting Sobolev-type inequalities
Csaba Farkas, Alexandru Kristály, Ágnes Mester
Let be an -dimensional compact Riemannian manifold with Ric. If supports an AB-type critical Sobolev inequality with Sobolev con…