A rigidity result for global Mumford-Shah minimizers in dimension three
نویسندگان
چکیده
We study global Mumford-Shah minimizers in R , introduced by Bonnet as blow-up limits of Mumford-Shah minimizers. We prove a new monotonicity formula for the energy of u when the singular set K is contained in a smooth enough cone. We then use this monotonicity to prove that for any reduced global minimizer (u,K) in R, if K is contained in a half-plane and touching its edge, then it is the half-plane itself. This partially answers to a question of Guy David.
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