Weak convergence and cancellation

Details Weak convergence and cancellation Weak convergence and cancellation

2009-02-17

arxiv.org/abs/0902.2993v1

Calculus of Variations and Partial Differential Equations, Vol. 38, No 1-2, May 2010, pp 183-206

Mathematics

Differential Geometry

22 pages, with an appendix by Raanan Schul and the second author

Scientific paper

In this article, we study the relationship between the weak limit of a sequence of integral currents in a metric space and the possible Hausdorff limit of the sequence of supports. Due to cancellation, the weak limit is in general supported in a strict subset of the Hausdorff limit. We exhibit sufficient conditions in terms of topology of the supports which ensure that no cancellation occurs and that the support of the weak limit agrees with the Hausdorff limit of the supports. We use our results to prove countable $\hm^m$-rectifiability of the Gromov-Hausdorff limit of sequences of Lipschitz manifolds $M_n$ all of which are $\lambda$-linearly locally contractible up to some scale $r_0$. In an appendix, written by Raanan Schul and the second author, it is shown that the Gromov-Hausdorff limit need not be countably $\hm^m$-rectifiable if the $M_n$ have a common local geometric contractibility function which is only concave (and not linear). We also relate our results to work of Cheeger-Colding on the limits of noncollapsing sequences of manifolds with nonnegative Ricci curvature.

Affiliated with

Also associated with

No associations

Rating

Weak convergence and cancellation 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 Weak convergence and cancellation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak convergence and cancellation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-127420