Affiliation:
1. Mathematics Department , University of Massachusetts , Amherst , MA 01003 , USA
2. Department of Geometry and Topology and Institute of Mathematics (IMAG) , University of Granada , 18071 Granada , Spain
Abstract
Abstract
Given
ε
0
>
0
{{\varepsilon}_{0}>0}
,
I
∈
ℕ
∪
{
0
}
{I\in\mathbb{N}\cup\{0\}}
and
K
0
,
H
0
≥
0
{K_{0},H_{0}\geq 0}
,
let X be a complete Riemannian 3-manifold with
injectivity radius
Inj
(
X
)
≥
ε
0
{\operatorname{Inj}(X)\geq{\varepsilon}_{0}}
and with the supremum
of absolute sectional curvature at most
K
0
{K_{0}}
, and let
M
↬
X
{M\looparrowright X}
be a complete
immersed surface of constant mean curvature
H
∈
[
0
,
H
0
]
{H\in[0,H_{0}]}
with index at most I.
For such
M
↬
X
{M\looparrowright X}
, we prove a structure theorem
which describes how the interesting ambient geometry of the immersion is organized
locally around at most I points of M,
where the norm of the second fundamental form takes on large local maximum values.
Funder
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Agencia Estatal de Investigación
Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía
Subject
Applied Mathematics,Analysis
Cited by
2 articles.
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