Some generalizations of Calabi compactness theorem

Details Some generalizations of Calabi compactness theorem Some generalizations of Calabi compactness theorem

2011-12-16

arxiv.org/abs/1112.3703v1

Mathematics

Differential Geometry

20 pages, submitted

Scientific paper

In this paper we obtain generalized Calabi-type compactness criteria for complete Riemannian manifolds that allow the presence of negative amounts of Ricci curvature. These, in turn, can be rephrased as new conditions for the positivity, for the existence of a first zero and for the nonoscillatory-oscillatory behaviour of a solution $g(t)$ of $g"+Kg=0$, subjected to the initial condition $g(0)=0$, $g'(0)=1$. A unified approach for this ODE, based on the notion of critical curve, is presented. With the aid of suitable examples, we show that our new criteria are sharp and, even for $K\ge 0$, in borderline cases they improve on previous works of Calabi, Hille-Nehari and Moore.

Affiliated with

Also associated with

No associations

Rating

Some generalizations of Calabi compactness theorem 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 Some generalizations of Calabi compactness theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some generalizations of Calabi compactness theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-136325