A Reilly formula and eigenvalue estimates for differential forms

Details A Reilly formula and eigenvalue estimates for differential forms A Reilly formula and eigenvalue estimates for differential forms

2010-03-03

arxiv.org/abs/1003.0817v1

Journal of Geometric Analysis 22, 3 (2011) 620-640

Mathematics

Differential Geometry

22 pages

Scientific paper

10.1007/s12220-010-9161-0

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.

Affiliated with

Also associated with

No associations

Rating

A Reilly formula and eigenvalue estimates for differential forms 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 Reilly formula and eigenvalue estimates for differential forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Reilly formula and eigenvalue estimates for differential forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-684715