Morse's index formula in VMO for compact manifolds with boundary
Abstract
In this paper, we study Vanishing Mean Oscillation vector fields on a compact manifold with boundary. Inspired by the work of Brezis and Niremberg, we construct a topological invariant - the index - for such fields, and establish the analogue of Morse's formula. As a consequence, we characterize the set of boundary data which can be extended to nowhere vanishing VMO vector fields. Finally, we show briefly how these ideas can be applied to (unoriented) line fields with VMO regularity, thus providing a reasonable framework for modelling a surface coated with a thin film of nematic liquid crystals.
Keywords
Cite
@article{arxiv.1407.1707,
title = {Morse's index formula in VMO for compact manifolds with boundary},
author = {Giacomo Canevari and Antonio Segatti and Marco Veneroni},
journal= {arXiv preprint arXiv:1407.1707},
year = {2015}
}
Comments
27 pages, 2 figures. This is a revised version of an older work; new results have been added, proofs of some classical results have been omitted, and the plan of the paper has been modified