Abstract 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 } \Gamma=\{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.
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This content will become publicly available on February 21, 2025
Predicting Mutational Effects on Ca 2+ -Activated Chloride Conduction of TMEM16A Based on a Simulation Study
- Award ID(s):
- 2142727
- NSF-PAR ID:
- 10502305
- Publisher / Repository:
- J Am Chem Soc
- Date Published:
- Journal Name:
- Journal of the American Chemical Society
- Volume:
- 146
- Issue:
- 7
- ISSN:
- 0002-7863
- Page Range / eLocation ID:
- 4665 to 4679
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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