Curvatures of Sobolev metrics on diffeomorphism groups

Details Curvatures of Sobolev metrics on diffeomorphism groups Curvatures of Sobolev metrics on diffeomorphism groups

2011-09-08

arxiv.org/abs/1109.1816v2

Mathematics

Analysis of PDEs

Written for "Geometric and Algebraic Structures in Mathematics," a conference in celebration of Dennis Sullivan's 70th birthda

Scientific paper

Many conservative partial differential equations correspond to geodesic equations on groups of diffeomorphisms. Stability of their solutions can be studied by examining sectional curvature of these groups: negative curvature in all sections implies exponential growth of perturbations and hence suggests instability, while positive curvature suggests stability. In the first part of the paper we survey what we currently know about the curvature-stability relation in this context and provide detailed calculations for several equations of continuum mechanics associated to Sobolev $H^0$ and $H^1$ energies. In the second part we prove that in most cases (with some notable exceptions) the sectional curvature assumes both signs.

Affiliated with

Also associated with

No associations

Rating

Curvatures of Sobolev metrics on diffeomorphism groups 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 Curvatures of Sobolev metrics on diffeomorphism groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Curvatures of Sobolev metrics on diffeomorphism groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-476522