Decoupling for surfaces with radial symmetry

Abstract

We utilise the two principles of decoupling introduced in [arXiv:2407.16108] to prove decoupling for two types of surfaces exhibiting radial symmetry. The first type are surfaces of revolution in $\mathbb R^n$ generated by smooth surfaces in $\mathbb R^3$. The second type of surfaces are graphs of trivariate homogeneous smooth functions of a nonzero degree.