Aidan Backus

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20192023

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math.DG2023

Regularity of sets of least perimeter in Riemannian manifolds

Aidan Backus

We give a short proof, in the tradition of the classical work of de Giorgi and Miranda on flat space, that the reduced boundary of a set of least perimeter in a Riemannian manifold…

math.CA2023

The fractal uncertainty principle via Dolgopyat's method in higher dimensions

Aidan Backus, James Leng, Zhongkai Tao

We prove a fractal uncertainty principle with exponent $\frac{d}{2} - δ + ε$ , $ε > 0$ , for Ahlfors--David regular subsets of $R^{d}$ with dimension $δ$ whi…