Harnack Inequalities for Critical 4-manifolds with a Ricci Curvature Bound
Differential Geometry
2013-09-16 v3
Abstract
We study critical Riemannian 4-manifolds with a lower bound on Ricci curvature, but no a priori analytic constraints such as on Sobolev constants. We derive elliptic-type estimates for the local curvature radius, which itself controls sectional curvature. The primary method is construction of blow-ups of degenerating metrics, followed by a geometric/topological triviality result from a previous work.
Keywords
Cite
@article{arxiv.1309.0863,
title = {Harnack Inequalities for Critical 4-manifolds with a Ricci Curvature Bound},
author = {Brian Weber},
journal= {arXiv preprint arXiv:1309.0863},
year = {2013}
}
Comments
The third uploaded version corrects some potentially confusing typographical errors. No material adjustments were made