Moduli spaces of critical Riemannian metrics in dimension four
Copyright policy )Moduli spaces of critical Riemannian metrics in dimension four
We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With certain geometric assumptions, the moduli space can be compactified by adding metrics with orbifold singularities. Similar results were obtained previously for Einstein metrics, but our analysis differs substantially from the Einstein case in that we do not assume any pointwise Ricci curvature bound.
24 pages, to appear in Advances in Mathematics
- Massachusetts Institute of Technology United States
Mathematics - Differential Geometry, Mathematics(all), Mathematics - Analysis of PDEs, Anti-self-dual metrics, Differential Geometry (math.DG), Moduli problems for differential geometric structures, Critical metrics, Orbifolds, FOS: Mathematics, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, Mathematics(all), Mathematics - Analysis of PDEs, Anti-self-dual metrics, Differential Geometry (math.DG), Moduli problems for differential geometric structures, Critical metrics, Orbifolds, FOS: Mathematics, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Analysis of PDEs (math.AP)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).43 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!