9 citations · 40 across the 13 of their papers we have counts for
16 papers
Inverse Garment Design with Visual Agents
Nanxiang Jiang, Yunuo Chen, Zeng Tao +5
We study the problem of inverse garment design, reconstructing simulation-ready 3D outfits with arbitrary layers from a single image, with visual agents. Unlike differentiable opti…
Lebesgue measure of distance sets and ball inflation
Shengwen Gan, Bochen Liu, Shukun Wu
We give an alternative proof of the result of Guth-Iosevich-Ou-Wang on the Falconer distance conjecture: if a compact set in the plane has Hausdorff dimension , the…
Lower bounds for parameter-dependent oscillatory integrals and Fourier frames on hypersurfaces
Shilei Fan, Bochen Liu
We prove lower bounds for Fourier transforms of surface measures $$|\widehat{ψ\,dσ}(ξ)| \gtrsim_{ψ, K, σ, R_0} σ(B(p, |ξ|^{-1})), \text{ given }p\in K\Subset\{ψ>0\} ,\ \vec{n}_{p}\…
Some constructions of restricted Kakeya sets
Cheng Chen, Jianbin Li, Longhui Li +4
In this paper, we consider Kakeya sets with the additional restriction that centers of the unit line segments belong to a given set. In particular, for every uncountable Borel set…
Lebesgue measure of distance sets with regular pins and multi-scale Mizohata-Takeuchi-type estimates
Bochen Liu
Suppose are Borel sets in the plane, , , and has equal Hausdorff and packing dimension. We prove tha…
Orthogonal projection, dual Furstenberg problem, and discretized sum-product
Longhui Li, Bochen Liu
In this paper we come up with a dual version of the Furstenberg problem and obtain partial results via estimates of orthogonal projections. Examples are also discussed. Moreo…
Falconer distance problem on Riemannian manifolds
Changbiao Jian, Bochen Liu, Yakun Xi
We prove that on a -dimensional Riemannian manifold, the distance set of a Borel set has a positive Lebesgue measure if $$\dim_{\mathcal{H}}(E)>\frac d2+\frac14+\frac{1-(-1)…
Improved local smoothing estimate for the wave equation in higher dimensions
Chuanwei Gao, Bochen Liu, Changxing Miao +1
In this paper, we establish the sharp -broad estimate for a class of phase functions satisfying the homogeneous convex conditions. As an application, we obtain improved local sm…
Square function estimates and Local smoothing for Fourier Integral Operators
Chuanwei Gao, Bochen Liu, Changxing Miao +1
We prove a variable coefficient version of the square function estimate of Guth--Wang--Zhang. By a classical argument of Mockenhaupt--Seeger--Sogge, it implies the full range of sh…
Microlocal decoupling inequalities and the distance problem on Riemannian manifolds
Alex Iosevich, Bochen Liu, Yakun Xi
We study the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the result of Guth-Iosevich-Ou-Wang for the distance set in the pla…
Pinned distance problem, slicing measures and local smoothing estimates
Alex Iosevich, Bochen Liu
We improve the Peres-Schlag result on pinned distances in sets of a given Hausdorff dimension. In particular, for Euclidean distances, with we prove…
Group actions, the Mattila integral and applications
Bochen Liu
The Mattila integral, developed by Mattila, is the main tool in the study of the Falc…
An elementary approach to simplexes in thin subsets of Euclidean space
Allan Greenleaf, Alex Iosevich, Bochen Liu +1
We prove that if the Hausdorff dimension of , , is greater than then the -d…
Falconer distance problem, additive energy and Cartesian products
Alex Iosevich, Bochen Liu
A celebrated result due to Wolff says if is a compact subset of , then the Lebesgue measure of the distance set is positive if the Haus…
A group-theoretic viewpoint on Erdos-Falconer problems and the Mattila integral
A. Greenleaf, A. Iosevich, B. Liu +1
We obtain nontrivial exponents for Erd\H os-Falconer type problems. Let denote the set of distinct congruent -dimensional simplexes determined by -tuples of poin…
On radii of spheres determined by subsets of Euclidean space
Bochen Liu
In this paper we consider the problem of how large the Hausdorff dimension of needs to be in order to ensure that the radii set of -dimensional spheres determ…