Line Integral Along Rectifiable Curves in Metric Spaces
Автор: Young Measures
Загружено: 2022-05-18
Просмотров: 290
Описание:
Integral of functions and vector fields along curves, known as line integal, path integral, or curve integral, has many applications in physics (work, flow across a curve, etc.)
In complex analysis they are called contour integral and play an important role: Cauchy's integral theorem, residue theorem, etc. (See also Green's theorem.)
Today, we
\begin{itemize}
\item define line integrals on rectifiable curves in arbitrary metric spaces,
\item relate it to integration against the Hausdorff-1 measure, and
\item discuss its application to the theory of Sobolev functions on metric measure spaces.
\end{itemize}
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