6 papers
On the Weyl tube formula for nonlocal perimeters
Serena Dipierro, Jack Thompson, Enrico Valdinoci
We study the asymptotic behaviour of the nonlocal perimeter of tubular neighbourhoods. For a closed submanifold of Euclidean space, we show that a suitable rescaling of t…
Volumetric density estimates for nonlocal minimal surfaces
Mateusz Kwaśnicki, Jack Thompson
In this article, we prove that viscosity subsolutions to nonlocal mean curvature-type equations satisfy universal volumetric estimates at all scales. Our results hold for general s…
A half-space theorem for nonlocal minimal surfaces
Matteo Cozzi, Jack Thompson
We establish a half-space theorem à la Hoffman and Meeks for nonlocal minimal surfaces. Differently from the classical case, our result holds in every dimension.
The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis
Serena Dipierro, Mateusz Kwaśnicki, Jack Thompson +1
We revisit a Harnack inequality for antisymmetric functions that has been recently established for the fractional Laplacian and we extend it to more general nonlocal elliptic opera…
Quantitative stability for the nonlocal overdetermined Serrin problem
Serena Dipierro, Giorgio Poggesi, Jack Thompson +1
We establish quantitative stability for the nonlocal Serrin overdetermined problem, via the method of the moving planes. Interestingly, our stability estimate is even better than t…
Some nonlocal formulas inspired by an identity of James Simon
Serena Dipierro, Jack Thompson, Enrico Valdinoci
Inspired by a classical identity proved by James Simons, we establish a new geometric formula in a nonlocal, possibly fractional, setting. Our formula also recovers the classical c…