A negative mass theorem for the 2-Torus

Details A negative mass theorem for the 2-Torus A negative mass theorem for the 2-Torus

2007-11-21

arxiv.org/abs/0711.3489v2

Mathematics

Spectral Theory

Scientific paper

10.1007/s00220-008-0644-9

For a closed surface M with metric g, the Robin mass m(p) at the point p is the value of the Green function G(p,q) at p=q after the logarithmic singularity has been removed. The Laplacian-mass is the average value of the Robin mass, minus the value of the Robin mass for the round sphere of the same area. The Laplacian-mass is a spectral invariant which is a natural analog of the ADM mass for asymptotically flat manifolds. We show that if M is a torus, then the minimum value of the Laplacian-mass on the conformal class of g is negative. It is attained by a (smooth) metric for which one gets a sharp logarithmic Hardy-Littlewood-Sobolev inequality and Onofri-type inequality. If the flat metric in the conformal class is sufficiently long and thin, then the minimizer for the Laplacian-mass is non-flat.

Affiliated with

Also associated with

No associations

Rating

A negative mass theorem for the 2-Torus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A negative mass theorem for the 2-Torus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A negative mass theorem for the 2-Torus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-310064