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On planar Nikodym-type sets
Alan Chang, Mingfeng Chen, Shaoming Guo +3
Nikodym constructed a measure-zero Borel set in the plane that contains a punctured line segment passing through each point in the unit square. Fenton and Falconer asked whether a…
Restriction and Kakeya maximal estimates in
Tainara Borges, Tiklung Chan, Mingfeng Chen +3
By combining the planebrush argument of Katz and Zahl \cite{katz21} with the decoupling-incidence method of Wang and Wu \cite{WangWu2024}, we derive new bounds for the Fourier rest…
Oscillatory integral operators and variable Schrödinger propagators: beyond the universal estimates
Mingfeng Chen, Shengwen Gan, Shaoming Guo +3
We consider a class of Hörmander-type oscillatory integral operators in for odd with real analytic phase. We derive weak conditions on the phase which ens…
The dichotomy of Nikodym sets and local smoothing estimates for wave equations
Mingfeng Chen, Shaoming Guo
We show that Nikodym sets and local smoothing estimates for linear wave equations form a dichotomy: If Nikodym sets for a family of curves exist, then the related maximal operator…
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.