Appendix B. The Stokes Theorem on Complete Manifolds
Appendix B gives a detailed proof of a version (due to M.P. Gaffney, 1954) of the Stokes theorem on complete Riemannian manifolds.
Keywords: Complete Riemannian manifold; Stokes theorem; Friedrichs mollifier; Hodge operator; Hopf-Rinow theorem.
Let (
M,
g) be an
n-dimensional orientable complete Riemannian manifold and
the Hodge operator. For each
we set
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