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math.AP2023★ 2 cited
A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow
Antoni Kijowski, Qing Liu, Ye Zhang +1
This paper is concerned with a PDE approach to horizontally quasiconvex (h-quasiconvex) functions in the Heisenberg group based on a nonlinear second order elliptic operator. We di…
math.DG2023
Asymptotically mean value harmonic functions in sub-Riemannian and RCD settings
Tomasz Adamowicz, Antoni Kijowski, Elefterios Soultanis
We consider weakly and strongly asymptotically mean value harmonic (amv-harmonic) functions on subriemannian and RCD settings. We demonstrate that, in non-collapsed RCD-spaces with…