Unformatted text preview: C , suppose that for all holomorphic functions F : D (0 , 1) → U the function f ◦ F is subharmonic. Prove that f itself is subharmonic. (4) Let f ∈ C 2 ( U ) for some open U ⊂ C . Suppose f is subharmonic. Show that Δ f ≥ 0 on U . (Hint: Taylor expansion) Now suppose Δ f > 0 on U , show that f is subharmonic. (Hint: f has no local maxima) Finally suppose Δ f ≥ 0 on U , show that f is subharmonic. (Hint: Consider Δ( f + ±  z  2 )). 1...
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 Spring '09
 Calculus, Derivative, Analytic function, Holomorphic function, nonconstant subharmonic functions

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