Gromov-Lawson Tunnels with Estimates

TL;DR

This paper generalizes the construction of positive scalar curvature tunnels from three-dimensional manifolds to higher dimensions, providing estimates and methods for creating arbitrarily narrow tunnels of prescribed length.

Contribution

It extends previous work by developing a higher-dimensional construction of positive scalar curvature tunnels with explicit estimates and narrowness control.

Findings

Construction of positive scalar curvature tunnels in arbitrary dimensions.

Existence of arbitrarily narrow tunnels with prescribed length.

Explicit estimates for tunnel size and volume.

Abstract

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.