KnowraLiouville's theoremLinked fromLinked fromThe 14 pages that link to Liouville's theorem, each with the reason it gives.All 14Broader topic 1Related 9Compared with 4Schwarz lemmaCompared with: It also turns boundedness into rigidity, but on the whole plane rather than the disk.Weierstrass factorization theoremCompared with: It shows how a growth restriction can sharply limit the functions allowed by a zero set.Émile PicardCompared with: It restricts entire functions by boundedness, whereas Picard restricts them by omitted values.Phragmén–Lindelöf principleCompared with: It shows how a global boundedness condition alone controls functions on the whole plane.