Loading...
Deformations of Q-curvature II
Lin, Yueh-Ju Yuan, Wei
Lin, Yueh-Ju
Yuan, Wei
Files
Loading...
Preprint
Adobe PDF, 293.7 KB
Authors
Other Names
Location
Time Period
Advisors
Original Date
Digitization Date
Issue Date
2022-02-11
Type
Article
Genre
Keywords
Differential geometry,Mathematics
Subjects (LCSH)
Citation
Lin, YJ., Yuan, W. Deformations of Q-curvature II. Calc. Var. 61, 74 (2022). https://doi.org/10.1007/s00526-021-02181-5
Abstract
This is the second article of a sequence of research on deformations of Q-curvature. In the previous one, we studied local stability and rigidity phenomena of Q-curvature. In this article, we mainly investigate the volume comparison with respect to Q-curvature. In particular, we show that volume comparison theorem holds for metrics close to strictly stable positive Einstein metrics. This result shows that Q-curvature can still control the volume of manifolds under certain conditions, which provides a fundamental geometric characterization of Q-curvature. Applying the same technique, we derive the local rigidity of strictly stable Ricci-flat manifolds with respect to Q-curvature, which shows the non-existence of metrics with positive Q-curvature near the reference metric.
Table of Contents
Description
Click on the DOI to access this article from publisher. Preprint version available.
Publisher
Springer
Journal
Book Title
Series
Calculus of Variations and Partial Differential Equations;2022
Digital Collection
Finding Aid URL
Use and Reproduction
Archival Collection
PubMed ID
DOI
ISSN
1432-0835