Get an easy, step-by-step explanation of the Gauss Divergence Theorem designed to make this important vector calculus concept ...

In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector fields that can have singularities at every point of a compact set whose Minkowski content of codimension ...

Trilemmas are everywhere. Defined as either a forced single choice among three unfavorable options or a two-out-of-three-only choice among favorable options, trilemmas involve trade-offs. The latter, ...

This is a preview. Log in through your library . Abstract The Serre duality for a holomorphic vector bundle over a compact, complex manifold still holds over a compact, strongly pseudo-convex manifold ...

Many prominent phenomena originate from geometrical effects rather than from local physics. For example, the 'hairy ball' (HB) theorem asserts that a hairy sphere cannot be combed without introducing ...

You might be surprised to learn that you can’t comb the hairs flat on a coconut without creating a cowlick. Perhaps even more surprising, this silly claim with an even sillier name, the “hairy ball ...