What determines the shape?We have seen examples of both flat and curved surfaces. Think about a soap bubble -- soap bubbles are round like balls. Their shape is determined by surface tension (*) (like the stretch in a balloon).
We will see that the shape of a membrane is strongly influenced by the amount of effort -- energy -- it takes to change the shape of the surface. Membranes tend to find the shapes that have the least energy.
A simple example is an uninflated balloon. This will lie flat on the table. It won't magically inflate because it takes energy to inflate the balloon -- this energy comes from the effort you have to put into blowing.