Geodesic
$K$-mean convex and $K$-outward minimizing sets
Annalisa Cesaroni1 ; Matteo Novaga2 orcid
1Università di Padova, Italy
2Università di Pisa, Italy
Interfaces and free boundaries, Tome 24 (2022) no. 1, pp. 35-61

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DOI

We consider the evolution of sets by nonlocal mean curvature and we discuss the preservation along the flow of two geometric properties, which are the mean convexity and the outward minimality. The main tools in our analysis are the level set formulation and the minimizing movement scheme for the nonlocal flow. When the initial set is outward minimizing, we also show the convergence of the (time integrated) nonlocal perimeters of the discrete evolutions to the nonlocal perimeter of the limit flow.
DOI : 10.4171/ifb/466
Classification : 53-XX, 35-XX, 49-XX
Mots-clés : Nonlocal curvature flows, mean convexity, nonlocal minimal surfaces, level set flow, minimizing movements

Annalisa Cesaroni  1   ; Matteo Novaga  2

1 Università di Padova, Italy
2 Università di Pisa, Italy 
Annalisa Cesaroni; Matteo Novaga. $K$-mean convex and $K$-outward minimizing sets. Interfaces and free boundaries, Tome 24 (2022) no. 1, pp. 35-61. doi: 10.4171/ifb/466
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