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math.DG2020★ 2 cited
Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature
Zoltán M. Balogh, Alexandru Kristály
By using optimal mass transport theory we prove a sharp isoperimetric inequality in metric measure spaces assuming an asymptotic volume growth at infinity. Our res…
math.AP2020
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(…