Level set flow in 3D steady gradient Ricci solitons
Given a nontrivial 3-dimensional steady gradient Ricci soliton, if the scalar curvature has decay order between - b and - a for some a ∈ ( 0 , 1 ] , b ≥ a , then the umbilical ratio of the level set of the potential function lies in the class O ( r 6 a - 8 a 2 b ) ∩ O ( r 2 b - 4 a ) .
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| Veröffentlicht in: | Manuscripta mathematica 2019-01, Vol.158 (1-2), p.223-234 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Given a nontrivial 3-dimensional steady gradient Ricci soliton, if the scalar curvature has decay order between
-
b
and
-
a
for some
a
∈
(
0
,
1
]
,
b
≥
a
, then the umbilical ratio of the level set of the potential function lies in the class
O
(
r
6
a
-
8
a
2
b
)
∩
O
(
r
2
b
-
4
a
)
. |
|---|---|
| ISSN: | 0025-2611 1432-1785 |
| DOI: | 10.1007/s00229-018-1020-5 |