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Let      D D       be a bounded convex domain in      C n {{\mathbf {C}}^n}      . We prove that the set      V V       of fixed points of a holomorphic map      f : D →  D f:D \to D       is a complex submanifold of      D D       and, if      V V       is not empty,      V V       is a holomorphic retract of      D D      .

Points fixes d’applications holomorphes dans un domaine borné convexe de 𝐶ⁿ