Abstract
While much is known about the invariants of conformal manifolds, the same cannot be said for the invariants of submanifolds in conformal geometries. Codimension one embedded submanifolds (or hypersurfaces) are important for applications to geometric analysis and physics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
L. Andersson, P. Chrusciel, H. Friedrich, On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein’s field equations. Commun. Math. Phys. 149, 587–612 (1992)
P. Avilés, R.C. McOwen, Complete conformal metrics with negative scalar curvature in compact Riemannian manifolds. Duke Math. J. 56, 395–398 (1988)
P. Avilés, R.C. McOwen, Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds. J. Differ. Geom. 27, 225–239 (1988)
C. Fefferman, C.R. Graham, The Ambient Metric. Annals of Mathematics Studies, vol. 178 (Princeton University Press, Princeton, 2012), x+113 pp
A.R. Gover, Almost Einstein and Poincaré–Einstein manifolds in Riemannian signature. J. Geom. Phys. 60, 182–204 (2010). arXiv:0803.3510.
A.R. Gover, Y. Vyatkin (in progress)
A.R. Gover, A. Waldron, Boundary calculus for conformally compact manifolds. Indiana Univ. Math. J. 63(1), 119–163 (2014). arXiv:1104.2991
C. Loewner, L. Nirenberg, Partial differential equations invariant under conformal or projective transformations, in Contributions to Analysis (Academic, New York, 1974)
Acknowledgements
Prior to this work, A.R. Gover had discussions about this problem with Fernando Marques and then Pierre Albin and Rafe Mazzeo. We are indebted for the insights so gained. The first author is supported by Marsden grant 10-UOA-113.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Gover, A.R., Waldron, A. (2015). Submanifold Conformal Invariants and a Boundary Yamabe Problem. In: González, M., Yang, P., Gambino, N., Kock, J. (eds) Extended Abstracts Fall 2013. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-21284-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-21284-5_4
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-21283-8
Online ISBN: 978-3-319-21284-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)