Related papers: Supercritical discrete restriction estimates for f…
We prove a Fourier restriction result, uniform over a certain collection of reference measures, for some indices in the Stein-Tomas range.
The purpose of this article is twofold. On the one hand, we prove asymptotic formulas for the quantitative distribution of rational points on any smooth non-split projective quadratic surface. We obtain the optimal error term for the real…
We prove qualitative estimates on the total curvature of closed minimal hypersurfaces in closed Riemannian manifolds in terms of their index and area, restricting to the case where the hypersurface has dimension less than seven. In…
We derive some estimates for stable minimal hypersurfaces in $R^{n+1}$. The estimates are related to recent proofs of Bernstein theorems for complete stable minimal hypersurfaces in $R^{n+1}$ for $3\le n\le 5$ by Chodosh-Li,…
In this paper, we study the restriction problem for one class of hypersurfaces with vanishing curvature in $\mathbb{R}^n$ with $n$ being odd. We obtain an $L^2-L^p$ restriction estimate, which is optimal except at the endpoint. Furthermore,…
We consider restriction analogues on hypersurfaces of the uniform Sobolev inequalities in Kenig, Ruiz, and Sogge and the resolvent estimates in Dos Santos Ferreira, Kenig, and Salo.
We prove matching asymptotic lower and upper bounds on the variances of the intrinsic volumes and the number of $k$-faces of $d$-dimensional random beta-polytopes. Using Stein's methods, we establish central limit theorems for the intrinsic…
The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and…
We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of the irreducible components of the hypersurface. As an…
We establish lower bounds on the ambient dimension for an intersection of hypersurfaces to have a dense collection of ``level $\ell$" points, in the sense introduced by Arnold-Shimura, given as a polynomial in the numbers of hypersurfaces…
In this paper, we discuss some theoretical results and properties of a discrete version of the Birnbaum-Saunders distribution. We present a proof of the unimodality of this model. Moreover, results on moments, quantile function, reliability…
For smooth open toric varieties, we establish strong approximation off infinity with Brauer-Manin obstruction.
The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we provide expressions for its moments of arbitrary order…
We prove an endpoint version of the Stein-Tomas restriction theorem, for a general class of measures, and with a strengthened Lorentz space estimate. A similar improvement is obtained for Stein's estimate on oscillatory integrals of…
We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…
We present explicit expressions for the Maurer-Cartan forms of the superdiffeomorphism group associated to a super Riemann surface. As an application to superconformal field theory, we use these forms to evaluate the effective action for…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
The Generalised Baker--Schmidt Problem (1970) concerns the $f$-dimensional Hausdorff measure of the set of $\psi$-approximable points on a nondegenerate manifold. There are two variants of this problem, concerning simultaneous and dual…
We obtain sharp mixed norm Strichartz estimates associated to mixed homogeneous surfaces in $\mathbb{R}^3$. Both cases with and without a damping factor are considered. In the case when a damping factor is considered our results yield a…
We develop a numerical scheme for subdiffusion of variable exponent by combining the $L2-1_\sigma$ temporal discretization with finite element spatial approximation. In existing works, determining the superconvergence points requires…