Nonlocal minimal surfaces are unique for all but countably many parameters in any strictly increasing family of exterior data, and arbitrarily small perturbations yield smooth minimizers in one dimension beyond the critical threshold.
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Nonlocal minimal surfaces are generically unique, and smooth in one extra dimension
Nonlocal minimal surfaces are unique for all but countably many parameters in any strictly increasing family of exterior data, and arbitrarily small perturbations yield smooth minimizers in one dimension beyond the critical threshold.