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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.AP2024
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…