From the 1 of 7 linked papers with an AI index.
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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…
Liouville's theorems for Lévy operators
Tomasz Grzywny, Mateusz KwaÅnicki
Let be a Lévy operator. A function is said to be harmonic with respect to if in an appropriate sense. We prove Liouville's theorem for positive functions har…
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…
Hardy inequalities and nonlocal capacity
Tomasz Grzywny, Julia Lenczewska
In this article, we introduce and study capacities related to nonlocal Sobolev spaces, with focus on spaces corresponding to zero-order nonlocal operators. In particular, we prove…