Subharmonic function

Okay kiddo, let's talk about subharmonic functions. Imagine you have a bouncy ball and you want to throw it up in the air, the ball will go up and then come back down. Now imagine there's a magic power that you can use to lift the ball up again before it hits the ground. This is a bit like what happens in subharmonic functions.

A subharmonic function is a bit like a bouncing ball but instead of a ball, it's a function that you put in a number, and it gives you another number as an output. But the important thing about a subharmonic function is that it's a bit tricky, like a magic power. Think of it like this: if you imagine that the function is the height of the bouncing ball, then the subharmonic function is like a force that lifts the ball up again before it hits the ground.

Let's say you have a function that goes up and down like a bouncing ball, and let's say the function always goes down a little faster than it goes up. This means that if you were to plot the function on a graph, it would look a bit like a hill with a steep slope on one side and a gentle slope on the other.

Now, if you imagine that the height of this function is the height of the ball, then a subharmonic function would be like applying a magic power to make the ball jump up a little higher each time it comes down. This magic power works by lifting the ball up just enough that it doesn't hit the ground before heading back up the hill.

So, in summary, subharmonic functions are like magic powers that can lift up a function that's going down a little faster than it's going up, before it hits the ground. They work like bouncing balls that you can keep bouncing without ever letting them fully hit the ground.