On the Variation of the Fractional Mean Curvature under the Effect of C1,α Perturbations
نویسندگان
چکیده
In this brief note we study how the fractional mean curvature of order s ∈ (0, 1) varies with respect to C diffeomorphisms. We prove that, if α > s, then the variation under a C diffeomorphism Ψ of the s-mean curvature of a set E is controlled by the C norm of the Jacobian of Ψ. When α = 1 we discuss the stability of these estimates as s → 1− and comment on the consistency of our result with the classical framework.
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