Growth Estimates for Generalized Harmonic Forms on Noncompact Manifolds with Geometric Applications
Shihshu Walter Wei · arXiv (Cornell University) · 2020
We introduce Condition W $\,$(1.2) for a smooth differential form $ω$ on a complete noncompact Riemannian manifold $M$. We prove that $ω$ is a harmonic form on $M$ if and only if $ω$ is both closed and co-closed on $M\, ,$ where $ω$ has $2$-balanced growth either for $q=2$, or for $1 < q( e 2) < 3\, $ with $ω$ satisfying Condition W $\,$(1.2). In particular, every $L^2$ harmonic form, or every $L^q$ harmonic form, $1