Abstract: Sard's Theorem is a fundamental result in Mathematical Analysis and Differential Geometry. In its simplest form it states the following fact: If at every point of a given set the gradient of a smooth map between vector spaces (or manifolds) has rank strictly less than the dimension of the map's target, then this set is mapped into a null set. Intuitively, this means that at such "critical points", a smooth map (locally) "squashes" the image into a lowerdimensional set, which is not seen by the Lebesgue measure. This short lecture will given a brief introduction to this result and its geometric meaning.
Sard's Theorem“
28.05.2025 09:30 - 09:50
Organiser:
R. I. Boţ
Location: