Square-integrability of solutions of the Yamabe equation
Differential Geometry
2014-01-10 v1 Analysis of PDEs
Abstract
We show that solutions of the Yamabe equation on certain n-dimensional non-compact Riemannian manifolds which are bounded and L^p for p=2n/(n-2) are also L^2. This L^p-L^2-implication provides explicit constants in the surgery-monotonicity formula for the smooth Yamabe invariant in a previous article of the authors. As an application we see that the smooth Yamabe invariant of any 2-connected compact 7-dimensional manifold is at least 74.5. Similar conclusions follow in dimension 8 and in dimensions at least 11.
Keywords
Cite
@article{arxiv.1111.2780,
title = {Square-integrability of solutions of the Yamabe equation},
author = {Bernd Ammann and Mattias Dahl and Emmanuel Humbert},
journal= {arXiv preprint arXiv:1111.2780},
year = {2014}
}