Renormalized weighted volume and conformal fractional Laplacians

María del Mar González

Vol. 257 (2012), No. 2, 379–394

DOI: 10.2140/pjm.2012.257.379

Abstract

We give a notion of renormalized weighted volume in the setting of conformal geometry following the ideas of Fefferman and Graham. Indeed, it is a precise term in the asymptotic expansion near the boundary for a weighted volume related to the conformal fractional Laplacian operator and fractional-order Q-curvature.

Keywords

fractional Laplacian, renormalized volume, fractional curvature

Mathematical Subject Classification 2010

Primary: 35J70, 53A30, 35R11

Milestones

Received: 19 July 2011

Revised: 27 January 2012

Accepted: 27 February 2012

Published: 4 July 2012