If I dont believe in you, do you exist?

Do we influence our mutual existences?

 

If a tree falls and no one is around is said to make no sound, then do we exist ourselves without being perceived by others? Or is our capacity for existence predicated on our own individual perceptions?

 

Does God exist if we perceive him to? Do we exist if God perceives us? Is it a mutually beneficial relationship of dependency?

 Do aliens exist on other planets because they believe we do and, consequently, does our belief in extraterrestrial life determine their existence?