In what sense we can approximate subharmonic functions by smooth subharmonic functions? This is not clear for me. I thank if you answer me. A priori, the definition of subharmonic …

Feb 11, 2015 · 4) The modulus of a holomorphic function is subharmonic. In particular, $|f (z)|$ and $|g (z)|$ are subharmonic. 5) Linear combinations of subharmonic functions with positive …

Oct 20, 2015 · With that, a subharmonic function should satisfy the maximum principle, the strong one, i.e. if there is x0 ∈ Ω for which the maximum on ¯ Ω is u(x0), then u is constant.

Feb 2, 2020 · The proof follows from the fact that if f(z0) ≠ 0 f (z 0) ≠ 0, there is an analytic logarithm of log f log f near z0 z 0 and log|f| = R log f log | f | = ℜ log f is harmonic so we have …

Aug 29, 2013 · Can you give me two examples of Subharmonic, Plurisubharmonic? (and not Subharmonic, not Plurisubharmonic) . Then prove that your examples. I'm looking forward to …

Mar 12, 2015 · Subharmonic function equivalent non-negative laplacian Ask Question Asked 10 years, 10 months ago Modified 7 years, 8 months ago

Jul 17, 2017 · Mean-value theorem for subharmonic functions: Ask Question Asked 8 years, 6 months ago Modified 8 years, 1 month ago

Apr 16, 2016 · I noticed this post and this paper, which gives a version of Liouville's theorem for subharmonic functions and the reference of its proof, but I think there must be an easier proof …

If $u$ is harmonic, prove that $|Du|^2$ is subharmonic. Ask Question Asked 11 years ago Modified 11 years ago

Dec 26, 2017 · My question might sound stupid, but here we go. Recall that a function u u is called subharmonic (superharmonic) if Δu ≥ 0(≤ 0) Δ u ≥ 0 (≤ 0). 1) Why is the former called …