Terence L. J. Harris

activity

20162026

most citedImproved decay of conical averages of the Fourier transform

10 citations · 48 across the 18 of their papers we have counts for

collaborators

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13 papers · 1 filter

math.CA2026

The divergence set for the wave equation in higher dimensions

Xiumin Du, Terence L. J. Harris, Jianhui Li

It is shown that if $u$ solves the wave equation in $R^{4 + 1}$ with initial data $u (\cdot, 0) = u_{0} (\cdot) \in H^{s}$ and $\partial_{t} u (\cdot, 0) = u_{1} (\cdot) \in H^{s - 1}$ , whe…

math.CA2026

On the parabolic Hausdorff dimension of orthogonal projections

Terence L. J. Harris, Pertti Mattila

For Borel sets $A \subset R^{n} \times R$ we prove lower bounds for the parabolic Hausdorff dimension of the orthogonal projections of $A$ on generic $m$ -dimensional…

math.CA2023★ 2 cited

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…

math.CA2022★ 1 cited

Length of sets under restricted families of projections onto lines

Terence L. J. Harris

Let $γ : I \to S^{2}$ be a $C^{2}$ curve with $det (γ, γ^{'}, γ^{''})$ nonvanishing, and for each $θ \in I$ let $ρ_{θ}$ be orthogonal projection onto the span of $γ (θ)$ . It is shown that if $A \…

math.CA2022★ 3 cited

On restricted projections to planes in $R^{3}$

Shengwen Gan, Shaoming Guo, Larry Guth +3

Let $γ : [0, 1] \to S^{2}$ be a non-degenerate curve in $R^{3}$ , that is to say, $det (γ (θ), γ^{'} (θ), γ " (θ)) \neq = 0$ . For each $θ \in [0, 1]$ , let $V_θ=γ(θ)^\pe…

math.CA2022★ 2 cited

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…

math.CA2021

Fourier dimension of the cone

Terence L. J. Harris

It is shown that the cone in $R^{d + 1}$ has Fourier dimension $d - 1$ . This verifies a conjecture of Fraser and Kroon.

math.CA2021★ 3 cited

Restricted families of projections onto planes: The general case of nonvanishing geodesic curvature

Terence L. J. Harris

It is shown that if $γ : [a, b] \to S^{2}$ is $C^{3}$ with $det (γ, γ^{'}, γ^{''}) \neq = 0$ , and if $A \subseteq R^{3}$ is a Borel set, then $\dim π_θ (A) \geq \min\left\{ 2,\dim A, \fra…

math.CA2021★ 5 cited

On the Fourier dimension of $(d, k)$ -sets and Kakeya sets with restricted directions

Jonathan M. Fraser, Terence L. J. Harris, Nicholas G. Kroon

A $(d, k)$ -set is a subset of $R^{d}$ containing a $k$ -dimensional unit ball of all possible orientations. Using an approach of D.~Oberlin we prove various Fourier dimension…

math.CA2021

Low dimensional pinned distance sets via spherical averages

Terence L. J. Harris

An inequality is derived for the average $t$ -energy of pinned distance measures, where $0 < t < 1$ . This refines Mattila's theorem on distance sets to pinned distance sets, and giv…

math.CA2020★ 2 cited

Fourier decay of fractal measures on hyperboloids

Alex Barron, M. Burak Erdogan, Terence L. J. Harris

Let $μ$ be an $α$ -dimensional probability measure. We prove new upper and lower bounds on the decay rate of hyperbolic averages of the Fourier transform $μ$ . More precisely…

math.CA2019★ 4 cited

Improved bounds for restricted projection families via weighted Fourier restriction

Terence L. J. Harris

It is shown that if $A \subseteq R^{3}$ is a Borel set of Hausdorff dimension $dim A \in (3/2, 5/2)$ , then for a.e. $θ \in [0, 2 π)$ the projection $π_{θ} (A)$ of $A$ onto the 2-d…

math.CA2018★ 5 cited

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.

The divergence set for the wave equation in higher dimensions

On the parabolic Hausdorff dimension of orthogonal projections

Vertical projections in the Heisenberg group for sets of dimension greater than 3

Length of sets under restricted families of projections onto lines

On restricted projections to planes in R3

A Euclidean Fourier-analytic approach to vertical projections in the Heisenberg group

Fourier dimension of the cone

Restricted families of projections onto planes: The general case of nonvanishing geodesic curvature

On the Fourier dimension of (d,k)-sets and Kakeya sets with restricted directions

Low dimensional pinned distance sets via spherical averages

Fourier decay of fractal measures on hyperboloids

Improved bounds for restricted projection families via weighted Fourier restriction

An a.e. lower bound for Hausdorff dimension under vertical projections in the Heisenberg group

On restricted projections to planes in $R^{3}$

On the Fourier dimension of $(d, k)$ -sets and Kakeya sets with restricted directions