Norm-minimizing surfaces in link complements with nonzero linking numbers remain norm-minimizing after Dehn filling along their boundaries except for finitely many rays when there are two components.
Monogr., Clarendon Press, Oxford
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The effect of link Dehn surgery on the Thurston norm
Norm-minimizing surfaces in link complements with nonzero linking numbers remain norm-minimizing after Dehn filling along their boundaries except for finitely many rays when there are two components.