|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
On Neck Singularities for 2-Convex Mean Curvature Flow | | Alexander Majchrowski
; | | Date: |
9 Jun 2017 | | Abstract: | In this paper we are dealing with mean curvature flow with surgeries of
two-convex hypersurfaces. The main focus is to expand on the discussion in
Section $3$ of Mean Curvature Flow with Surgeries of Two-Convex Hypersurfaces
by Huisken and Sinestrari. Firstly we wish to establish how the neck detection
lemma allows us to detect necks where the cross sections will be diffeomorphic
to $S^{n-1}$. We then want to see how we are able to glue these cross sections
together with full control on their parametrisation - for this we will show we
can use a harmonic spherical parametrisation using the techniques from
Hamiltons paper, Four-manifolds with Positive Isotropic Curvature. We then
introduce the notion of a normal and maximal necks, this allows us to obtain
uniqueness, existence and overlapping properties for normal parametrisations on
$(epsilon,k)$-cylindrical hypersurface necks. Lastly given a neck
$N:S^{n-1} imes[a,b] omathcal{M}$ we want to see that in the case that
either $a=infty$ or $b=infty$ that this forces them to both to be $infty$
and that we are left with a solid tube $S^{n-1} imes S^1$. | | Source: | arXiv, 1706.2818 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER