We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general theory to characterize the limits of s-fractional mean curvature flows as (Formula presented.) and (Formula presented.) In analogy with the s-fractional mean curvature flows, we introduce the notion of s-Riesz curvature flows and characterize its limit as (Formula presented.) Eventually, we discuss the limit behavior as (Formula presented.) of the flow generated by a regularization of the r-Minkowski content.
Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows / Cesaroni, A.; De Luca, L.; Novaga, M.; Ponsiglione, M.. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 46:7(2021), pp. 1344-1371. [10.1080/03605302.2021.1875485]
Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows
Cesaroni A.;Novaga M.;Ponsiglione M.
2021
Abstract
We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general theory to characterize the limits of s-fractional mean curvature flows as (Formula presented.) and (Formula presented.) In analogy with the s-fractional mean curvature flows, we introduce the notion of s-Riesz curvature flows and characterize its limit as (Formula presented.) Eventually, we discuss the limit behavior as (Formula presented.) of the flow generated by a regularization of the r-Minkowski content.File | Dimensione | Formato | |
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