On the Isoperimetric Problem for Radial Log-convex Densities
نویسنده
چکیده
E e as balls centered at the origin, provided m ∈ [0, m0) for some (potentially computable) m0 > 0; this affirmatively answers conjecture [RCBM, Conjecture 3.12] for such values of the weighted volume parameter. We also prove that the set of weighted volumes such that this characterization holds true is open, thus reducing the proof of the full conjecture to excluding the possibility of bifurcation values of the weighted volume parameter. Finally, we show the validity of the conjecture when V belongs to a C-neighborhood of c|x| (c > 0).
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