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Article Dans Une Revue Communications in Analysis and Geometry Année : 2021

Bernstein-Moser-type results for nonlocal minimal graphs

Matteo Cozzi
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Luca Lombardini
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Résumé

We prove a flatness result for entire nonlocal minimal graphs having some partial derivatives bounded from either above or below. This result generalizes fractional versions of classical theorems due to Bernstein and Moser. Our arguments rely on a general splitting result for blow-downs of nonlocal minimal graphs. Employing similar ideas, we establish that entire nonlocal minimal graphs bounded on one side by a cone are affine. Moreover, we show that entire graphs having constant nonlocal mean curvature are minimal, thus extending a celebrated result of Chern on classical CMC graphs.
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Dates et versions

hal-03621402 , version 1 (27-05-2024)

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Matteo Cozzi, Alberto Farina, Luca Lombardini. Bernstein-Moser-type results for nonlocal minimal graphs. Communications in Analysis and Geometry, 2021, 29 (4), pp.761-777. ⟨10.4310/cag.2021.v29.n4.a1⟩. ⟨hal-03621402⟩
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