Hodge theory on ALGmanifolds

Gao Chen, Jeff Viaclovsky, Ruobing Zhang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We develop a Fredholm theory for the Hodge Laplacian in weighted spaces on ALG∗ manifolds in dimension four. We then give several applications of this theory. First, we show the existence of harmonic functions with prescribed asymptotics at infinity. A corollary of this is a non-existence result for ALG∗ manifolds with non-negative Ricci curvature having group Γ = { e } at infinity. Next, we prove a Hodge decomposition for the first de Rham cohomology group of an ALG∗ manifold. A corollary of this is vanishing of the first Betti number for any ALG∗ manifold with non-negative Ricci curvature. Another application of our analysis is to determine the optimal order of ALG∗ gravitational instantons.

Original languageEnglish (US)
Pages (from-to)189-227
Number of pages39
JournalJournal fur die Reine und Angewandte Mathematik
Issue number799
StatePublished - Jun 1 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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