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math.AP2024
Alexandrov Theorem for nonlocal curvature
Wojciech Cygan, Tomasz Grzywny
In this article we obtain a nonlocal version of the Alexandrov Theorem which asserts that the only set with sufficiently smooth boundary and of constant nonlocal mean curvature is…
math.AP2023
Asymptotics and geometric flows for a class of nonlocal curvatures
Wojciech Cygan, Tomasz Grzywny, Julia Lenczewska
We consider a family of nonlocal curvatures determined through a kernel which is symmetric and bounded from above by a radial and radially non-increasing profile satisfying an inte…
math.AP2022
Asymptotics of non-local perimeters
Wojciech Cygan, Tomasz Grzywny
We introduce a notion of non-local perimeter which is defined through an arbitrary positive Borel measure on which integrates the function . Such defini…