A First Course in Complex Analysis · Problem 6.3.11

Power Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · harmonic-functions

Problem

Prove that, if

u

is harmonic and bounded on

\mathbb{C}

, then

u

is constant. Hint. Use Theorem 6.1.7 and Liouville's Theorem (Corollary 5.3.4).