CMC hypersurfaces with bounded Morse index
Differential Geometry
2021-02-10 v3
Abstract
We develop a bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular we show that convergence always occurs with multiplicity one, which implies that the minimal blow-ups (bubbles) are all catenoids. We also provide bounds on the area of separating CMC surfaces of bounded (Morse) index and use this, together with the previous results, to bound their genus.
Cite
@article{arxiv.2102.02651,
title = {CMC hypersurfaces with bounded Morse index},
author = {Theodora Bourni and Ben Sharp and Giuseppe Tinaglia},
journal= {arXiv preprint arXiv:2102.02651},
year = {2021}
}
Comments
Fixed a tex-compiling issue