10 citations · 48 across the 18 of their papers we have counts for
19 papers
The divergence set for the wave equation in higher dimensions
Xiumin Du, Terence L. J. Harris, Jianhui Li
It is shown that if solves the wave equation in with initial data and , whe…
On the parabolic Hausdorff dimension of orthogonal projections
Terence L. J. Harris, Pertti Mattila
For Borel sets we prove lower bounds for the parabolic Hausdorff dimension of the orthogonal projections of on generic -dimensional…
Maximal inequalities and the decay of Fourier transforms of measures
Terence L. J. Harris
It is shown that Schrödinger maximal inequalities over fractals are equivalent to the decay rates of Fourier transforms of fractal measures over the paraboloid. A similar con…
Vertical projections in the Heisenberg group for sets of dimension greater than 3
Terence L. J. Harris
It is shown that vertical projections in the Heisenberg group of sets of dimension strictly greater than 3 almost surely have positive area. The proof uses the point-plate incidenc…
Length of sets under restricted families of projections onto lines
Terence L. J. Harris
Let be a curve with nonvanishing, and for each let be orthogonal projection onto the span of . It is shown that if $A \…
On restricted projections to planes in
Shengwen Gan, Shaoming Guo, Larry Guth +3
Let be a non-degenerate curve in , that is to say, . For each , let $V_θ=γ(θ)^\pe…
A Euclidean Fourier-analytic approach to vertical projections in the Heisenberg group
Terence L. J. Harris
An improved a.e. lower bound is given for Hausdorff dimension under vertical projections in the first Heisenberg group, with respect to the Carnot-Carathéodory metric. This improve…
Fourier dimension of the cone
Terence L. J. Harris
It is shown that the cone in has Fourier dimension . This verifies a conjecture of Fraser and Kroon.
Restricted families of projections onto planes: The general case of nonvanishing geodesic curvature
Terence L. J. Harris
It is shown that if is with , and if is a Borel set, then $\dim π_θ (A) \geq \min\left\{ 2,\dim A, \fra…
On the Fourier dimension of -sets and Kakeya sets with restricted directions
Jonathan M. Fraser, Terence L. J. Harris, Nicholas G. Kroon
A -set is a subset of containing a -dimensional unit ball of all possible orientations. Using an approach of D.~Oberlin we prove various Fourier dimension…
Low dimensional pinned distance sets via spherical averages
Terence L. J. Harris
An inequality is derived for the average -energy of pinned distance measures, where . This refines Mattila's theorem on distance sets to pinned distance sets, and giv…
Fourier decay of fractal measures on hyperboloids
Alex Barron, M. Burak Erdogan, Terence L. J. Harris
Let be an -dimensional probability measure. We prove new upper and lower bounds on the decay rate of hyperbolic averages of the Fourier transform . More precisely…
Dimension Distortion by Right Coset Projections in the Heisenberg Group
Terence L. J. Harris, Chi N. Y. Huynh, Fernando Roman-Garcia
We study the family of vertical projections whose fibers are right cosets of horizontal planes in the Heisenberg group, . We prove lower bounds for Hausdorff dimensio…
Improved bounds for restricted projection families via weighted Fourier restriction
Terence L. J. Harris
It is shown that if is a Borel set of Hausdorff dimension , then for a.e. the projection of onto the 2-d…
An a.e. lower bound for Hausdorff dimension under vertical projections in the Heisenberg group
Terence L. J. Harris
An improved a.e. lower bound is given for Hausdorff dimension under vertical projections in the first Heisenberg group.
Improved decay of conical averages of the Fourier transform
Terence L. J. Harris
An improved lower bound is given for the decay of conical averages of Fourier transforms of measures, for cones of dimension . The proof uses a weighted version of the br…
Refined Strichartz inequalities for the wave equation
Terence L. J. Harris
Some analogues of the Schrödinger refined Strichartz inequalities (Du, Guth, Li and Zhang) are obtained for the wave equation. These are used to improve the best known fracta…
Two-by-two upper triangular matrices and Morrey's conjecture
Terence L. J. Harris, Bernd Kirchheim, Chun-Chi Lin
It is shown that every homogeneous gradient Young measure supported on matrices of the form $\begin{pmatrix} a_{1,1} & \cdots & a_{1,n-1} & a_{1,n} \\ 0 & \cdots & 0 & a_{2,n} \end…
Upper semicontinuity of the lamination hull
Terence L. J. Harris
Let be a compact set, let be its rank-one convex hull, and let be its lamination convex hull. It is shown that the mapping $K…