Timewise-max function

From Diffgeom
Jump to: navigation, search

Definition

Let u:\R \times M \to \R be any continuous function. Then the timewise-max function of u is a map f:\R \to \R defined by:

f(t) = \sup_{x \in M} u(t,x)

When M is a compact manifold, we can replace \sup by \max.

Related notions