Journal article
Constant Q-curvature metrics on conic 4-manifolds
Advances in calculus of variations, Vol.15(2), pp.235-264
04/01/2022
DOI: 10.1515/acv-2019-0056
Abstract
We consider the constant
-curvature metric problem in a given
conformal class on a conic 4-manifold and study related differential
equations. We define subcritical, critical, and supercritical conic
4-manifolds. Following [M. Troyanov,
Prescribing curvature on compact surfaces with conical singularities,
Trans. Amer. Math. Soc. 324 1991, 2,
793–821] and [S.-Y. A. Chang and P. C. Yang,
Extremal metrics of zeta function determinants on 4-manifolds,
Ann. of Math. (2) 142 1995, 1, 171–212],
we prove the existence of constant
-curvature metrics in the subcritical
case. For conic 4-spheres with two singular points, we prove the uniqueness
in critical cases and nonexistence in supercritical cases. We also
give the asymptotic expansion of the corresponding PDE near isolated
singularities.
Details
- Title: Subtitle
- Constant Q-curvature metrics on conic 4-manifolds
- Creators
- Hao Fang - University of IowaBiao Ma - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Advances in calculus of variations, Vol.15(2), pp.235-264
- Publisher
- De Gruyter
- DOI
- 10.1515/acv-2019-0056
- ISSN
- 1864-8258
- eISSN
- 1864-8266
- Number of pages
- 30
- Grant note
- 426312 / Simons Foundation
- Language
- English
- Date published
- 04/01/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984241058502771
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