During the past two decades there has been active interplay between geometric measure
theory and Fourier analysis. This book describes part of that development, concentrating on …

Let G (d, n) be the Grassmannian manifold of n-dimensional subspaces of R d, and let π V:
R d→ V be the orthogonal projection. We prove that if μ is a compactly supported Radon …

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Analytic capacity and projections Page 1 DOI 10.4171/JEMS/1004 J. Eur. Math. Soc. 22,
4121–4159 © European Mathematical Society 2020 Alan Chang · Xavier Tolsa Analytic …

This paper is concerned with restricted families of projections in R 3. Let K⊂ R 3 be a Borel
set with Hausdorff dimension dim⁡ K= s> 1. If G is a smooth and sufficiently well-curved one …

We characterise the big pieces of Lipschitz graphs property in terms of projections. Roughly
speaking, we prove that if a large subset of an n-Ahlfors–David regular set E⊂ Rd has …

It is well known that a classical Fubini theorem for Hausdorff dimension cannot hold; that is,
the dimension of the intersections of a fixed set with a parallel family of planes do not …

THE UNIVERSITY OF CHICAGO BESICOVITCH SETS, RECTIFIABILITY, AND
PROJECTIONS A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVIS Page 1 …

Investigating unions of lines or unions of higher dimensional affine subspaces has been an
important field of geometric measure theory in the past decades. Studying them, one can …