2 citations · 2 across the 2 of their papers we have counts for
5 papers
On Convexity, Mid-Point Convexity and Hausdorff Measures of Sets
Shaoming Guo, Tian Lan, Yakun Xi
We give a complete characterization of the size of Borel sets that are mid-point convex but not (essentially) convex, in terms of their Hausdorff dimensions and Hausdorff measures.
Decoupling in for curves with Vanishing Curvature
Chandan Biswas, Maxim Gilula, Linhan Li +2
We expand the class of curves for which the decoupling conjecture holds for . Our class of curves includes all real-analytic r…
Improved Generalized Periods Estimates Over Curves on Riemannian Surfaces with Nonpositive Curvature
Emmett L. Wyman, Yakun Xi
We show that on compact Riemann surfaces of nonpositive curvature, the generalized periods, i.e. the -th order Fourier coefficients of eigenfunctions over a closed smooth…
Inner product of eigenfunctions over curves and generalized periods for compact Riemannian surfaces
Yakun Xi
We show that for a smooth closed curve on a compact Riemannian surface without boundary, the inner product of two eigenfunctions and restricted to , $|\int e_λ\o…
On Instability of the Nikodym Maximal Function bounds over Riemannian Manifolds
Christopher D. Sogge, Yakun Xi, Hang Xu
We show that, for odd , the bounds of Sogge and Xi for the Nikodym maximal function over manifolds of constant sectional curvature, are unstable with respect t…