7 papers
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…
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…
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 smooth surfaces in
Jianhui Li, Tongou Yang
For each , we prove decoupling inequalities in for the graphs of all bivariate polynomials of degree at most with bounded coefficients, with the decoupli…
A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in
Malabika Pramanik, Tongou Yang, Joshua Zahl
We resolve a conjecture of Fässler and Orponen on the dimension of exceptional projections to one-dimensional subspaces indexed by a space curve in . We do this by o…