arXiv subjects
Publications and source records attributed to Józef Dodziuk.
We give a characterization of Whitney forms on an $n$-simplex $σ$ and prove that for every real valued simplicial $k$-cochain $c$ on $σ$, the form $Wc$ is the unique differential $k$-form $φ$ on $σ$ with affine coefficients that pulls back to a constant form of degree $k$ on every $k$-face $τ$ of $σ$ and satisfies $\int_τ φ= $.
In an appendix to an earlier paper (cf. arXiv:1703.00984) we showed we showed how to construct tunnels of positive scalar curvature and of arbitrarily small length and volume connecting points in a \emph{three dimensional} manifold of \emph{constant sectional curvature}. Here we generalize the construction to arbitrary dimensions and require only positivity of the scalar curvature. This version contains an added section on existence of arbitrarily narrow tunnels of prescribed length.