8 papers · 1 filter
Decoupling for degenerate hypersurfaces
Jianhui Li, Tongou Yang
We utilise the two principles of decoupling introduced in arXiv:2407.16108 to prove the following conditional result: assuming uniform decoupling for graphs of polynomials in all d…
Decoupling for surfaces with radial symmetry
Jianhui Li, Tongou Yang
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 o…
Two principles of decoupling
Jianhui Li, Tongou Yang
We put forward a radial principle and a degeneracy locating principle of decoupling. The former generalises the Pramanik-Seeger argument used in the proof of decoupling for the lig…
Sharp decoupling for paraboloids
Tongou Yang
In this short expository note, we prove the following result, which is a special case of the main theorem in arXiv:2011.09451. For each and , we pro…
A multi-parameter cinematic curvature
Mingfeng Chen, Shaoming Guo, Tongou Yang
We state a multi-parameter cinematic curvature condition, and prove bounds for related maximal operators. In particular, we verify a local smoothing conjecture of Zahl.
Decoupling for mixed-homogeneous polynomials in
Jianhui Li, Tongou Yang
We prove decoupling inequalities for mixed-homogeneous bivariate polynomials, which partially answers a conjecture of Bourgain, Demeter and Kemp.