An invariant related to the existence of conformally compact Einstein fillings

Matthew J. Gursky; Qing Han; Stephan Stolz

An invariant related to the existence of conformally compact Einstein fillings

Differential Geometry 2018-01-16 v1

Authors: Matthew J. Gursky , Qing Han , Stephan Stolz

Abstract

We define an invariant for compact spin manifolds $X$ of dimension $4k$ equipped with a metric $h$ of positive Yamabe invariant on its boundary. The vanishing of this invariant is a necessary condition for the conformal class of $h$ to be the conformal infinity of a conformally compact Einstein metric on $X$ .

Keywords

spin manifold yamabe invariant conformally compact einstein metric conformal infinity invariant

Cite

@article{arxiv.1801.04474,
  title  = {An invariant related to the existence of conformally compact Einstein fillings},
  author = {Matthew J. Gursky and Qing Han and Stephan Stolz},
  journal= {arXiv preprint arXiv:1801.04474},
  year   = {2018}
}

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