Long time behavior of leafwise heat flow for Riemannian foliations

TL;DR

This paper proves that leafwise heat flow for Riemannian foliations on closed manifolds preserves smoothness at infinite time, impacting the understanding of harmonic forms and spectral sequences.

Contribution

It establishes the long-term smoothness preservation of leafwise heat flow for Riemannian foliations, with implications for metric spaces and spectral sequence analysis.

Findings

Leafwise heat flow preserves smoothness at infinite time.

Results influence the understanding of leafwise harmonic forms.

Impacts the analysis of the differentiable spectral sequence.

Abstract

For any Riemannian foliation F on a closed manifold M with an arbitrary bundle-like metric, leafwise heat flow of differential forms is proved to preserve smoothness on M at infinite time. This result and its proof have consequences about the space of bundle-like metrics on M, about the dimension of the space of leafwise harmonic forms, and mainly about the second term of the differentiable spectral sequence of F.