- In the
mathematical field of
geometric measure theory, the
coarea formula expresses the
integral of a
function over an open set in
Euclidean space in terms...
- In
Riemannian geometry, the
smooth coarea formulas relate integrals over the
domain of
certain mappings with
integrals over
their codomains. Let M , N...
-
which generalizes the
concept of
change of
variables in integration. The
coarea formula,
which generalizes and
adapts Fubini's
theorem to
geometric measure...
- the
coarea formula, Hölder’s
inequality and the
classical isoperimetric inequality. If the
function u {\displaystyle u} is
smooth enough, the
coarea formula...
-
sophisticated results from
mathematical analysis such as Sard's
theorem and the
coarea formula. In even
greater generality,
using the
Lebesgue theory as below...
- be
expressed as an
integral over the
surface areas using the
coarea formula, the
coarea formula contains a
correction factor that
accounts for how the...
- justification,
without relying on the
special coordinates of trigonometry, uses the
coarea formula.
Define a
function ρ : R 2 → R {\displaystyle \rho :\mathbb {R}...
-
apply the
machinery of
geometric measure theory; for that
approach see the
coarea formula. In this article, we
instead use a more
elementary definition, based...
- Eilenberg's inequality, also
known as the
coarea inequality is a
mathematical inequality for Lipschitz-continuous
functions between metric spaces. Informally...
- d{\boldsymbol {u}}} for all
compactly supported functions f.
Using the
coarea formula from
geometric measure theory, one can also
define the composition...
