Shaoming Guo

collaborators

3 papers

math.CA2026

Curved Kakeya problems and the projective geometry of paths

Shaoming Guo, Larry Guth, Arian Nadjimzadah +2

We introduce a general framework for curved Kakeya problems in $R^{n}$ , encompassing those arising from Hörmander-type oscillatory integrals. Every family of curves determin…

math.CA2023

$L^{p}$ integrability of functions with Fourier support on a smooth space curve

Shaoming Guo, Alex Iosevich, Ruixiang Zhang +1

We prove that if $f \in L^{p} (R^{k})$ with $p < (k^{2} + k + 2) /2$ satisfies that $f$ is supported on a small perturbation of the moment curve in $R^{k}$ , then $f$ is…

math.DG2023

Oscillatory integral operators on manifolds and related Kakeya and Nikodym problems

Song Dai, Liuwei Gong, Shaoming Guo +1

We consider Carleson-Sjölin operators on Riemannian manifolds that arise naturally from the study of Bochner-Riesz problems on manifolds. They are special cases of Hörmander-type o…

Curved Kakeya problems and the projective geometry of paths

Lp integrability of functions with Fourier support on a smooth space curve

Oscillatory integral operators on manifolds and related Kakeya and Nikodym problems

$L^{p}$ integrability of functions with Fourier support on a smooth space curve